Related papers: Regular elements determined by generalized inverse…
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings), and…
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…
The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural conditions on a finite inverse semigroup guaranteeing that neither…
Let $R$ be a ring. It is proved that an $R$-module $M$ is Baer (resp. dual Baer) if and only if every exact sequence $0\rightarrow X\rightarrow M\rightarrow Y\rightarrow 0$ with $Y\in$ Cog$(M_R)$ (resp. $X\in$ Gen$(M_R)$) splits. This shows…
We apply recent results on the rank of elements of rings to study the structure of generalized corner rings $aRa$, where $R$ is a unital ring and $a$ an element of $R$. We give a complete description of the structure of $aRa$ when $a^2$ has…
We study those rings in which all invertible elements are weakly nil-clean calling them {\it UWNC rings}. This somewhat extends results due to Karimi-Mansoub et al. in Contemp. Math. (2018), where rings in which all invertible elements are…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
A multiring ([Mar3]) is a kind of ring where is allowed the sum of two elements to be anon-empty subset of the structure instead of just one element -and an hyperring is a multiring with a strong distributive property. Thus a reduced…
Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…
What are all rings $R$ for which $R^*$ (the group of invertible elements of $R$ under multiplication) is an elementary abelian $p$-group? We answer this question for finite-dimensional commutative $k$-algebras, finite commutative rings,…
Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators affiliated with $M.$ We prove that if $A$ is a locally convex reflexive complete metrizable…
Let $A$ be a commutative noetherian ring and $I$ an ideal in $A$. We characterize algebraically when all the minimal primes of the associated graded ring $G_I A$ contract to minimal primes of $A/I$. This, applied to intersection theory,…
In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…
The notion of weighted $(b,c)$-inverse of an element in rings were introduced, very recently [Comm. Algebra, 48 (4) (2020): 1423-1438]. In this paper, we further elaborate on this theory by establishing a few characterizations of this…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component…
In what follows we generalize the notion of a complemented ring to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.
We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…
Let $p$ be a prime integer and $\mathbb{Z}_p$ be the ring of $p$-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group ${\rm…
The concept of integral as an inverse to that of derivation was already introduced for rings and recently also for lattices. Since semirings generalize both rings and bounded distributive lattices, it is natural to investigate integration…