Related papers: Unifying some classical results on Artinian rings …

In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…

We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…

In a recent paper of Alahmadi, Alkan and Lopez-Permouth, a ring R is defined to have no (simple) middle class if the injectivity domain of any (simple) R-module is the smallest or largest possible. Er, Lopez-Permouth and Sokmez use this…

We revisit, clarify, and generalise classical results of Dickson and (much later) Wagner on minimal Sym(n)- and Alt(n)-modules. We present a new, natural notion of 'modules with an additive dimension' covering at once the classical,…

Goldie's Theorem implies that a semiprime left Goldie ring is embeddable into a semisimple Artinian ring. On the other hand, there are domains that are not embeddable into division rings. A criterion for a semiprime ring being embeddable…

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations…

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…

We obtain criteria for when a ring with enough idempotents is left/right artinian or noetherian in terms of local criteria defined by the associated complete set of idempotents for the ring. We apply these criteria to object unital category…

The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately…

Gerstenhaber showed in 1961 that any commuting pair of n x n matrices over a field k generates a k-algebra A of k-dimension \leq n. A well-known example shows that the corresponding statement for 4 matrices is false. The question for 3…

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the…

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

Let $(R,\mathfrak{m},k)$ be a Noetherian local ring and let $M$ be a finitely generated $R$-module. The main focus of this paper is to give positive answers for some long-standing homological conjectures over the idealization ring $R\ltimes…

We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…

In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It…

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L^\infty-eigenvalues. We make use of some…

Let $R$ be a ring and $S$ a multiplicative subset of $R$. We introduce and study the notions of ($u$-)$S$-$w$-Noetherian modules and ($u$-)$S$-$w$-principal ideal modules. Some characterizations of these new concepts are given.

If $R$ is a commutative unital ring and $M$ is a unital $R$-module, then each element of $\operatorname{End}_R(M)$ determines a left $\operatorname{End}_{R}(M)[X]$-module structure on $\operatorname{End}_{R}(M)$, where…

In this paper we introduce new modules over the ring of ponderation functions, so we recover old results in harmonic analysis from the side of ring theory. Moreover, we prove that Laplace transform, Fourier transform and Hankel transform…

Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras…