Modules whose countably generated submodules are epimorphic images
Modules with semiregular endomorphism rings
We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.
Monoid rings that are firs.
It is well known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature.
Multirelative -theory and axioms for the -theory of rings.
-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
--coherent rings and Gorenstein graded modules
Let be a graded ring and be an integer. We introduce and study the notions of Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules by using the notion of special finitely presented graded modules. On -gr-coherent rings, we investigate the relationships between Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules. Among other results, we prove that any graded module in -gr (or gr-) admits a Gorenstein -FP-gr-injective (or Gorenstein -gr-flat) cover and preenvelope, respectively....
-Koszul algebras, a summary.
-strongly Gorenstein graded modules
Let be a graded ring and an integer. We introduce and study -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever . Many properties of the -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...
Natural dualities between abelian categories
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
Near-rings in which each prime factor is simple.
Near-rings with a special condition on idempotents.
New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.
A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.
Nil-extensions of completely simple semirings
A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.
Non-abelian cohomology of associative algebras. The -term exact sequence
Noncommutative deformations of modules.
Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
Let be a dg algebra over and let be a dg -bimodule. We show that under certain technical hypotheses on , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product and converges to the Hochschild homology of . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.
Normalizing the cyclic modules of Connes.
On a Class with Rings with Inverse Weak Algorithm.
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On algebras of strongly unbounded representation type.