A Bezout theorem for determinantal modules
A Cancellation Theorem for Artinian Local Algebras.
A Cancellation Theorem for Projective Modules in the Metastable Range.
A characterization of Prüfer rings.
A class of principal ideal rings arising from the converse of the Chinese remainder theorem.
A class of torsion-free abelian groups characterized by the ranks of their socles
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket -module is tensor a bracket group.
A contribution to the theory of modules over finite-dimensional linear algebras
A corollary to the Evans-Griffith Syzygy theorem
A differential criterion for complete intersections.
A Few Remarks on the Mohan Kumar Theorem
We give a simple geometric proof of Mohan Kumar's result about complete intersections.
A full uniform Artin-Rees theorem.
A General Resolution for Grade Four Gorenstein Ideals.
A generalization of reflexive rings
We introduce a class of rings which is a generalization of reflexive rings and -reversible rings. Let be a ring with identity and denote the Jacobson radical of . A ring is called -reflexive if for any , implies . We give some characterizations of a -reflexive ring. We prove that some results of reflexive rings can be extended to -reflexive rings for this general setting. We conclude some relations between -reflexive rings and some related rings. We investigate some extensions of...
A generalization of the Auslander transpose and the generalized Gorenstein dimension
Let be a left and right Noetherian ring and a semidualizing -bimodule. We introduce a transpose of an -module with respect to which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use to develop further the generalized Gorenstein dimension with respect to . Especially, we generalize the Auslander-Bridger formula to the generalized...
A generalization of the finiteness problem of the local cohomology modules
Let be a commutative Noetherian ring and an ideal of . We introduce the concept of -weakly Laskerian -modules, and we show that if is an -weakly Laskerian -module and is a non-negative integer such that is -weakly Laskerian for all and all , then for any -weakly Laskerian submodule of , the -module is -weakly Laskerian. In particular, the set of associated primes of is finite. As a consequence, it follows that if is a finitely generated -module and is an -weakly...
A generalization of Ulm subgroups
A generic approach to the structure of certain normal ideals
A homological proof of a theorem by Davis, Geramita, Orecchia giving the Cayley-Bacharach theorem.
A new algebraic criterion for shellability.
A new algorithm for the Quillen-Suslin theorem.