Related papers: Trivial Extensions Defined by Coherent-like Condit…
We investigate the behavior of four coherent-like conditions in regular conductor squares. In particular, we find necessary and sufficient conditions in order that a pullback ring be a finite conductor ring, a coherent ring, a generalized…
This paper deals with well-known extensions of the Prufer domain concept to arbitrary commutative rings. We investigate the transfer of these notions in trivial ring extensions (also called idealizations) of commutative rings by modules and…
The notion of trivial extension of a ring by a module has been extensively studied and used in ring theory as well as in various other areas of research like cohomology theory, representation theory, category theory and homological algebra.…
In this paper we investigate a categorical aspect of $n$-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) $n$-trivial extension of a category by a family of endofunctors. Among other results,…
In this paper, we consider five possible extensions of the Pr\"ufer domain notion to the case of commutative rings with zero divisors. We investigate the transfer of these Pr\"ufer-like properties between a commutative ring and its subring…
This paper deals with five extensions of the Pr\"ufer domain concept to commutative rings with zero divisors. We investigate the stability of these Pr\"ufer-like conditions under localization and homomorphic image. Our results generate new…
This paper investigates ideal-theoretic as well as homological extensions of the Prufer domain concept to commutative rings with zero divisors in an amalgamated duplication of a ring along an ideal. The new results both compare and contrast…
Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…
We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…
Given a ring $R$, we study the bimodules $M$ for which the trivial extension $R\propto M$ is morphic. We obtain a complete characterization in the case where $R$ is left perfect, and we prove that $R\propto Q/R$ is morphic when $R$ is a…
We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commutator. Then we use the topological structure of the minimal…
Let $R$ be a commutative ring with identity and $T(R)$ its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to…
In this paper, we define weakly coherent rings, and examine the transfer of these rings to homomorphic image, trivial ring extension, localization, and direct product. These results provide examples of weakly coherent rings that are not…
We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution…
We study the interplay between the notions of $n$-coherent rings and finitely $n$-presented modules, and also study the relative homological algebra associated to them. We show that the $n$-coherency of a ring is equivalent to the thickness…
This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…