* Rings with nondiscrete ideal topologies*,
Proc. Amer. Math. Soc. ** 21**
(1969), 357-362.

* Subsemigroups of amenable groups*, Proc. Amer. Math. Soc. ** 21** (1969),
363-364.

* Prime ideal structure in commutative rings*, Trans. Amer. Math. Soc.
** 142** (1969), 43-60.

* Commutative rings with identity have ring topologies* (with J. O.
Kiltinen), Bull. Amer. Math. Soc. ** 76** (1970), 419-420.

* Totally integrally closed rings and extremal spaces*, Pac. J. Math.
** 32** (1970), 767-779.

* Rings of continuous functions and totally integrally closed rings*,
Proc. Amer. Math. Soc. ** 25** (1970), 439-442.

* A class of perfect determinantal ideals* (with J. A. Eagon), Bull.
Amer. Math. Soc. ** 76** (1970), 1026-1029.

* Symbolic powers in Noetherian domains*, Illinois J. Math.
** 15** (1971), 9-27.

* The minimal prime spectrum of a commutative ring*, Canadian J. Math.
** 23** (1971), 749-758.

* Existence of topologies for commutative rings with identity*, Duke
Math. J. ** 38** (1971), 551-554.

* Cohen-Macaulay rings, invariant theory, and the generic perfection
of determinantal loci* (with J. A. Eagon), Amer. J. Math. ** 93** (1971),
1020-1058.

* Generically perfect modules are strongly generically perfect*, Proc.
London Math. Soc. ** 23** (1971), 477-488.

* Nonuniqueness of coefficient rings in a polynomial ring*, Proc.
Amer. Math. Soc. ** 34** (1972), 81-82.

* Rings of invariants of tori, Cohen-Macaulay rings generated by
monomials, and polytopes*, Annals of Math. ** 96** (1972), 318-337.

* Cohen-Macaulay modules*, in * Conference on Commutative Algebra
* (Lawrence, Kansas, 1972), Lecture Notes in Mathematics, No. ** 311**,
Springer-Verlag, Berlin, 1973, 120-152.

* Five theorems on Macaulay rings* (with L. J. Ratliff, Jr.), Pacific
J. Math. ** 44** (1973), 147-172.

* Expanded radical ideals and semiregular ideals*, Pacific J. Math.
** 44 **(1973), 553-568.

* Non-openness of loci in Noetherian rings*, Duke Math. J. ** 40**
(1973), 215-219.

* Grassmannians and their Schubert subvarieties are arithmetically
Cohen-Macaulay*, J. of Algebra ** 25** (1973), 40-57.

* Contracted ideals from integral extensions of regular rings*, Nagoya
Math. J. ** 51** (1973), 25-43.

* Properties of Noetherian rings stable under general grade
reduction*, Arch. Math. ** 24** (1973), 393-396.

* Criteria for equality of ordinary and symbolic powers of primes*,
Math. Zeitschr. ** 133** (1973), 53-65.

* Constraints on systems of parameters*, in *
Ring Theory - Proceedings
of the Oklahoma Conference*, Marcel-Dekker, New York, 1974, 121-61.

* R-sequences and indeterminates* (with J. A. Eagon), Quart. J. Math.
(Oxford) ** 25** (1974), 61-71.

* Actions of reductive groups acting on regular rings and
Cohen-Macaulay rings* (with

J. L. Roberts), Bull. Amer. Math. Soc.
** 80**
(1974), 281-284.

* Rings of invariants of reductive groups acting on regular rings are
Cohen-Macaulay* (with

J. L. Roberts), Advances in Math. ** 13** (1974),
115-175.

* The equicharacteristic case of some homological conjectures on
local rings*, Bull. Amer. Math. Soc. ** 80** (1974), 683-686.

* Grade-sensitive modules and perfect modules*, Proc. London Math.
Soc. ** 29** (1974), 55-76.

* On the Zariski-Lipman conjecture for homogeneous complete
intersections*, Proc. Amer. Math. Soc. ** 49** (1975), 261-262.

* Topics in the Homological Theory of Modules over Commutative Rings*,
Proceedings of the Nebraska Regional C.B.M.S. Conference, (Lincoln,
Nebraska, 1974), Amer. Math. Soc., Providence, 1975, 75 pp.

* Big Cohen-Macaulay modules and algebras and embeddability in rings
of Witt vectors*, in * Proceedings of the Queen's University
Commutative Algebra Conference* (Kingston, Ontario, Canada, 1975),
Queen's Papers in Pure and Applied Math., No. ** 42**, 1975, 106-195.

* An obstruction to lifting cyclic modules*, Pacific J. Math.
** 61** (1975), 457-463.

* The purity of the Frobenius and local cohomology* (with J. L.
Roberts), Advances in Math. ** 20** (1976), 117-172.

* Cyclic purity versus purity in excellent Noetherian rings*, Trans.
Amer. Math. Soc. ** 231** (1977), 463-488.

* The Zariski-Lipman conjecture in the graded case*, J. of Algebra
** 47**
(1977), 411-424.

* Cohen-Macaulay rings, combinatorics, and simplicial complexes*, in
* Proceedings of the Second Oklahoma Ring Theory Conference* (March
1976), Marcel-Dekker, New York, 1977, 171-223.

* Some applications of the Frobenius in characteristic 0*, Bull. Amer.
Math. Soc. ** 84** (1978), 886-912.

* Big and small Cohen-Macaulay modules*, in *
Proceedings of the Special
Session on Module Theory* (Seattle, Aug. 1977), Lecture Notes in
Mathematics No. ** 700**, Springer-Verlag, Berlin-Heidelberg-New York,
1979, 119-142.

* A Nullstellensatz with nilpotents and Zariski's main lemma on
holomorphic functions* (with

D. Eisenbud), J. of Algebra ** 58** (1979),
157-161.

* Principal ideal theorems*, in * Proceedings of the Waterloo Ring Theory
Conference/*, Lecture Notes in Mathematics,No. ** 734**, Springer-Verlag,
Berlin-Heidelberg-New York, 1979, 174-208.

* Pathological maximal R-sequences in quasilocal domains*, Portugaliae
Mathematica V. ** 38**, Fasc. 3-4 (1979), 33-36.

* Cohen-Macaulay rings and modules*, in * Proceedings of the
International Congress of Mathematicians*, Helsinki, Finland, V. ** I**,
Academia Scientiarum Fennica, 1980, 291-298.

* The dimension of an intersection in an ambient hypersurface*, in
* Proceedings of the First Midwest Algebraic Geometry Seminar*,
Chicago Circle, l980, Lecture Notes in Mathematics
No. ** 862**,
Springer-Verlag, Berlin-Heidelberg-New York, 1981, 93-106.

* Associated graded rings derived from integrally closed ideals and
the local homological conjectures*, in * Proceedings of the Conference
on Commutative Algebra* (at Rennes, France, May, 1981), 1-27.

* The local homological conjectures*, in
* Proceedings of the Durham
Symposium on Commutative Algebra*, London Math. Soc. Lecture Note
Series ** 72**, Cambridge Univ. Press, Cambridge, 1982, 32-55.

* Splitting theorems for quadratic ring extensions* (with J. E.
McLaughlin), Illinois J. of Math. ** 27** (1983), 94-103.

* The direct summand conjecture and canonical elements in local
cohomology modules*, J. of Algebra ** 84** (1983), 503-553.

* Euler characteristics over unramified regular local rings*, Illinois
J. Math.** 28** (1984), 281-288.

* Modules of finite projective dimension with negative intersection
multiplicities* (with S. P. Dutta and J. E. McLaughlin), Inventiones
Mathematicae ** 79** (1985), 253-291.

* Invariant theory of commutative rings*, in *
Proceedings of the Summer
Research Conference on Groups Actions on Rings* (Bowdoin, July
1984), Contemporary Mathematics Vol. ** 43**, Amer. Math. Soc.,
Providence, R. I., 1985, 161-179.

* The generic syzygies of linear forms* (with D. Laksov), Comm. in
Algebra ** 15** (1&2) (1987), 227-239.

* Intersection problems and Cohen-Macaulay modules*, in * Algebraic
Geoemetry*, Bowdoin 1985, Proc. of Symposia in Pure Math., Amer.
Math. Soc., Providence, R. I., 1987, 491-501.

* Tightly closed ideals* (with C. Huneke), Bull. Amer. Math. Soc.
** 18**
(1988), 45-48.

* The canonical module of a ring of invariants*, in * Invariant
Theory*, Contemp. Math. Vol. ** 88**, Amer. Math. Soc., Providence,
R.I., 1989, 43-83.

* Tight closure* (with C. Huneke), in * Commutative Algebra*,
Math. Sci. Research Inst. Publ. ** 15**, Springer-Verlag,
New York-Berlin-Heidelberg, 1989, 305-324.

* Tight closure and strong F-regularity* (with C. Huneke), Memoires de
la Societe Mathematiques de France, numero ** 38** (1989), 119-133.

* Tight closure, invariant theory, and the Briancon-Skoda theorem*
(with C. Huneke), J. Amer. Math. Soc. ** 3** (1990), 31-116.

* Absolute integral closures are big Cohen-Macaulay algebras in
characteristic p* (with

C. Huneke), Bull. Amer. Math. Soc. (New
Series) ** 24** (1991), 137-143.

* Tight closure and elements of small order in integral extensions*
(with C. Huneke), J. of Pure and Applied Alg. ** 71** (1991), 233-247.

* Infinite integral extensions and big Cohen-Macaulay algebras* (with
C. Huneke), Annals of Math. ** 135** (1992), 53-89.

* Phantom Homology* (with C. Huneke), Memoirs of the Amer. Math.
Soc., Vol. ** 103**, No. ** 490** (1993), 1-91.

* Localization of tight closure and and modules of finite phantom
projective dimension* (with

C. Huneke and I. Aberbach), J. Reine
Angew. Math. (Crelle's Journal) ** 434** (1993), 67-114.

* Indecomposable canonical modules and connectedness*
(with C. Huneke), in
* Commutative Algebra: Syzygies,
Multiplicities and Birational Algebra*,
Contemp. Math. ** 159**, Amer. Math. Soc.,
Providence, R. I., 1994, 197-208.

* Solid closure*, in * Commutative Algebra:
Syzygies, Multiplicities and Birational Algebra*,
Contemp. Math. ** 159**, Amer. Math. Soc.,
Providence, R. I., 1994, 103-172.

* Tight closure in equal characteristic,
big Cohen-Macaulay algebras, and solid closure*,
in * Commutative Algebra: Syzygies, Multiplicities
and Birational Algebra*, Contemp. Math. ** 159**,
Amer. Math. Soc., Providence, R. I., 1994, 173-196.

* Tight closure of parameter ideals and splitting in module-finite
extensions* (with C. Huneke),

J. of Algebraic Geometry ** 3** (1994),
599-672.

* F-regularity, test elements, and smooth base change* (with C.
Huneke), Trans. Amer. Math. Soc. ** 346** (1994), 1-62.

* Applications of the existence of big Cohen-Macaulay algebras* (with
C. Huneke), Advances in Math. ** 113** (1995), 45-117.

*The notion of tight closure in equal characteristic zero*, in
* Proc. of the CBMS Conference on Tight Closure and Its Applications *
(Fargo, North Dakota, July, 1995), Appendix to the notes on the main
lectures by Craig Huneke, C.B.M.S. Regional Conference Series, A.M.S.,
Providence, R.I., 1996.

* Failure of coherence in R^+ and finite Tor dimension* (with
I. M. Aberbach), J. of Pure and Applied Alg. ** 122 **
(1997), 171-184.

* The tight integral closure of a set of ideals*,
Journal of Algebra ** 230 ** (2000), 184-203.

* Localization and test exponents for tight closure * (with
C. Huneke), Michigan Math. J. ** 48 ** (2000), 305-329.

* Comparison of symbolic and ordinary powers of ideals * (with C.
Huneke), Inventiones Math. ** 174 ** (2002) 349-369.

* Presentation depth and the Lipman-Sathaye Jacobian theorem *,
Homology, Homotopy and Applications (International Press,
Cambridge, MA) ** 4 ** (2002) 295-314.

* Big Cohen-Macaulay algebras in dimension three via Heitmann's
theorem *, Journal of Algebra ** 254 ** (2002) 395-408.

* Parameter-like sequences and extensions of tight closure*, in
Commutative Ring Theory and Applications (Proc. of the Fourth International
Conference, held in Fez, Morocco, June 7-12, 2001), Marcel Dekker, New York,
2003, pp. 267-287.

* Diamond closure * (with J. Velez), in Algebra, Arithmetic and
Geometry with Applications, Papers from Shreeram S. Abhyankar's
70th Birthday Conference, Springer-Verlag,
Berlin - Heidelberg - New York, 2004, pp. 511-523.

* Tight closure theory and characteristic p methods* (with an
Appendix by Graham J. Leuschke), in
Trends in Commutative Algebra, MSRI Pubications **51**, Cambridge
University Press, Cambridge, England, 2004, pp. 181-210.

* Lower bounds for Betti numbers of special extensions *
(with B. Richert), Journal of Pure and Applied Algebra ** 201 ** (2005)
328-339.

* Fine behavior of symbolic powers of ideals * (with Craig Huneke), Illinois J. Math. ** 51 ** (2007) 171-183.

* Homological conjectures, old and new*, Illinois J. Math. ** 51
** (2007) 151-169.

* Finiteness properties of Lyubeznik's F-modules *
Contemporary Math. ** 448** (2007) 119-127.

* The Frobenius structure of local cohomology * (with F.\ Enescu),
Algebra & Number Theory ** 2} ** (2008) 721-754.

* Quasilength, latent regular sequences, and content of local cohomology *
(with Craig Huneke), Journal of Algebra ** 322 ** (2009) 3170-3193.

* Homological invariants of modules over contracting endomorphisms *
(with L. Avramov, S. Iyengar, and Y. Yao), Math. Annalen,
** 353 ** (2012) 275-291.

* Ideals generated by quadratic polynomials * (with T. Ananyan), Math. Res. Lett. ** 19 ** (2012) 233-244.

* Test exponents for modules of finite phantom projective dimension * (with Y. Yao), Illinois J. Math.
** 56 ** (2012) 1095-1107.

* Local cohomology with support in a parameter ideal * (with Y. Yao), J. Pure and Applied Algebra, J. Pure Appl. Algebra ** 217 ** (2013) 664-671.

* F-purity, Frobenius splitting, and tight closure *, volume on Commutative Algebra honoring David Eisenbud,
471-484, Springer, New York, 2013.

* Cohen-Macaulay varieties, geomertric complexes and combinatorics *, in * The Mathematical Legacy of
Richard P. Stanley, * AMS, Providence, R.I., 2016, pp. 203-229.

* On the support of local cohomology via Frobenius,* (with L. Núñez-Betancourt),
Math. Res. Letters. ** 24 ** (2017), pp. 401-420.

* Homological conjectures and lim Cohen-Macaulay sequences},* in Homological and Computational Methods in Commutative Algebra, Springer INdAM Series 20, Springer, 2017, pp. 181-197. [In honor of Winfried Bruns. Primarily expository.]

* Continuous closure, natural closure, and axes closure *, with N. Epstein, Trans. Amer. Math. Soc. 370 (2018) 3315--3362.

* Content of local cohomology, parameter ideals, and robust algebras,* with W. Zhang,
Trans.Amer. Math.Soc. 370 (2018) 7789-7814.

* Finiteness properties and numerical behavior of local cohomology, * Comm.~Algebra 47 (2019) 1-11.
[In honor of Gennady Lyubeznik. Primarily expository.]

* Small subalgebras of polynomial rings and Stillman's conjecture, * with Tigran Ananyan, Journal of the Amer. Math. Soc.
33 (2020), 291-309.

* Strength conditions, small subalgebras, and Stillman bounds
in dimension ≤ 4,* with T. Ananyan, Trans. Amer. Math. Soc. 373 (2020) 4757-4806.

* Universal lex ideal approximations of extended Hilbert functions and Hamilton numbers, * with T.~Ananyan, Journal of Algebra
560 (2020) 1053-1074.

* The Eisenbud-Green-Harris conjecture for defect two quadratic ideals, *with S. Güntürkün,
Math. Research Letters, to appear.

* Faithfulness of top local cohomology modules in domains}, * with J.~Jeffries, Math. Res. Letters, to appear.

* The stable prime extension property}, * with J.~Jeffries, preprint.

* The F-rational signature and drops in the Hilbert-Kunz multiplicity * (with Y. Yao), preprint.

* An embedding theorem for modules of finite projective dimension * (with Y. Yao), preprint.

* Second coefficients of Hilbert-Kunz functions for domains * (with Y. Yao), preprint.

* Splitting of ^{e}M, strong F-regularity, and the existence of small Cohen-Macaulay modules, *
with Y. Yao, preprint.

* A weak embedding theorem for modules of finite phantom projective dimension* (with Y. Yao), preliminary preprint.

* Lim Cohen-Macaulay sequences * (with B. Bhatt and L. Ma), preliminary preprint.

* A weak embedding theorem for modules of finite phantom projective dimension * (with Y. Yao), in preparation.

* Homogeneous equational tight closure * (with N. Epstein), in preparation.

* Tight closure in equal characteristic zero* (with C. Huneke),
preprint, 204 pages.