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In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.
Dynamics of many supersymmetric monopoles are studied in the low energy approximation. A conjecture for the exact moduli space metric is given for all collections of fundamental monopoles of distinct type, and various partial confirmations…
We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not…
Various questions on Lie ideals of C*-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators,…
For a commutative unital ring $R$ with fixed ideals $I$ and $J$, we introduce and study $I$-prime $R$-modules and $(I, J)$-prime $R$-modules together with their duals $I$-coprime $R$-modules and $(I,J)$-coprime $R$-modules respectively. We…
We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andrews and Ballantine (J Combin Theory…
In this paper we introduce a new notion by the help of the idealizer. This new notion is the separator of a subset of a semigroup. We investigate the properties of the separator in an arbitrary semigroup and characterize the unitary…
In a previous paper we constructed rank and support variety theories for "quantum elementary abelian groups," that is, tensor products of copies of Taft algebras. In this paper we use both variety theories to classify the thick tensor…
In this paper, we prove Faltings' annihilator theorem for complexes over a CM-excellent ring. As an application, we give a complete classification of the t-structures of the bounded derived category of finitely generated modules over a…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…
In this article we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to "largeness". The first property is ID…
Sufficient conditions for an ideal $\mathcal I$ in $R\Mod$ to be covering are proved. This allows to obtain an alternative proof of the existence of phantom covers of modules. Our approach is inspired by an extension of the standard…
A famous result due to I. M. Isaacs states that if a commutative ring $R$ has the property that every prime ideal is principal, then every ideal of $R$ is principal. This motivates ring theorists to study commutative rings for which every…
We study, by means of mirror symmetry, the quantum geometry of the K\"ahler-class parameters of a number of Calabi-Yau manifolds that have $b_{11}=2$. Our main interest lies in the structure of the moduli space and in the loci corresponding…
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded…
These lectures give a self-contained introduction to supersymmetry from a modern perspective. Emphasis is placed on material essential to understanding duality. Topics include: central charges and BPS-saturated states, supersymmetric…
Let M be a factor of type II_\infty or II_1 having separable predual and let M-bar be the algebra of affiliated \tau-measureable operators. We characterize the commutator space [I,J] for sub-(M,M)-bimodules I and J of M-bar.
Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. In this paper, we introduce the notion of S-2-absorbing second submodules of M as a generalization of S-second submodules and…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.