BIBLIOGRAPHY FOR MELVIN HOCHSTER

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.

Continuous closure, natural closure, and axes closure , with N. Epstein, to appear in Trans. of the AMS.

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

Content of local cohomology, parameter ideals, and robust algebras, with W. Zhang, to appear in the Trans. of the AMS.

Homological conjectures and lim Cohen-Macaulay sequences, to appear in the Proceedings of the Conference on Homological and Computational Methods in Commutative Algebra (honoring Winfried Bruns), Cortona Italy, 2016.

Small subalgebras of polynomial rings and Stillman's conjecture, with Tigran Ananyan, preprint.

Strength conditions, small subalgebras, and Stillman bounds in dimension ≤ 4, with T. Ananyan, preprint.

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

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

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

The Frobenius complexity is finite (with F. Enescu), preprint.

Splitting of  eM, 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.