Related papers: Rings in which one-sided strongly $\pi$-regular el…
A semiring $S$ which is a union of rings is called completely regular, if moreover, it is orthodox then $S$ is called an orthoring. Here we study the orthorings $S$ such that $E^+(S)$ is a band semiring. Every band semiring is a spined…
We show that practically all the properties of almost perfect rings discovered by Bazzoni and Salce in "Almost perfect domains" (Colloq. Math. 95 (2) (2003), 285-301) for commutative rings hold in the non-commutative setting.
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A,…
A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. The class of stable rings includes the one-dimensional local Cohen-Macaulay rings of…
Which groups can be the group of units in a ring? This open question, posed by L\'{a}szl\'{o} Fuchs in 1960, has been studied by the authors and others with a variety of restrictions on either the class of groups or the class of rings under…
We give an explicit characterization of the solid rings of the fourth type, finishing a work by Bousfield and Kan in the 1970s. As a consequence of our methods, we give criteria to find the core of a ring and explicitly compute the core of…
Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $P$ be a parabolic subgroup of $G$, and $U_P$ its unipotent radical. We prove that if…
We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat $R$-module is semi-regular flat, if and only if every ideal…
We study a C*-dynamical system arising from the ring inclusion of the 2\times 2 integer matrices in the rational ones. The orientation preserving affine groups of these rings form a Hecke pair that is closely related to a recent…
We provide two new formulations of the separativity problem. First, it is known that separativity (and strong separativity) in von Neumann regular (and exchange) rings is tightly connected to unit-regularity of certain kinds of elements. By…
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
For linear non-uniform cellular automata (NUCA) which are local perturbations of linear CA over a group universe $G$ and a finite-dimensional vector space alphabet $V$ over an arbitrary field $k$, we investigate their Dedekind finiteness…
The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline…
We define and explore in details the class of GUSC rings, that are those rings whose non-invertible elements are uniquely strongly clean. These rings are a common generalization of the so-called USC rings, introduced by Chen-Wang-Zhou in J.…
Phase-sensitive measurements on a composite ring made of a superconductor of interest connected by a known singlet $s$-wave superconductor can unambiguously determine its pairing symmetry. In composite rings with epitaxial $\beta-$Bi$_2$Pd…
K\"othe's classical problem posed by G. K\"othe in 1935 asks to describe the rings $R$ such that every left $R$-module is a direct sum of cyclic modules (these rings are known as left K\"othe rings). K\"othe, Cohen and Kaplansky solved this…
We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.
Sufficient conditions on a space are given which guarantee that the $K$-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An…
Symplectic billiards were introduced by Albers and Tabachnikov as billiards in strictly convex bounded domains of the plane with smooth boundary having a specific law of reflection. This paper proves a rigidity result for symplectic…
We show that any strongly rigid-noetherian Huber ring $A$ is sheafy. In particular, we positively answer Problem~$31$ in the Nonarchimedean Scottish Book.