Related papers: Dedekind Superrings and Related Concepts

This paper studies the class group of graded integral domains. As an application, we state a decomposition theorem for class groups of semigroup rings. This recovers well-known results developed for the classic contexts of polynomial rings…

We introduce a complete radical formula for modules over non-commutative rings which is the equivalence of a radical formula in the setting of modules defined over commutative rings. This gives a general frame work through which known…

In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under direct summands. Several properties and characterizations have…

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduced the dual notion of z-submodules of M and some of extensions. Moreover, we investigate some properties of these classes of modules…

A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, the simple Dedekind domains form a second important class. We…

For a Dedekind domain $R$ with field of fractions $K$ a classical $R$-order in a semisimple $K$-algebra $A$ is an $R$-projective $R$-subalgebra $\Lambda$ of $A$ such that $K\Lambda=A$. We study differential graded $K$-algebras which are…

All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adele class space of a global field. After promoting F1 to a hyperfield K, we prove that a hyperring of the…

We introduce a new concept of a semiprime submodule. We show that a submodule of a finitely generated module over a commutative ring is semiprime if and only if it is radical, that is, an intersection of prime submodules. Using our notion,…

In 1995 Grillet defined the concept of a stratified semigroup and a stratified semigroup with zero. The present authors extended that idea to include semigroups with a more general base and proved, amongst other things, that finite…

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

We give examples of Frobenius algebras of rank two over ground Dedekind rings which are projective but not free and discuss possible applications of these algebras to link homology.

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudoreflection groups over Dedekind domains. In the special case of a principal ideal domain in which the group…

For an important class of arithmetic Dedekind domains O including the ring of integers of not totally complex number fields, we describe explicitly the group of linear characters of SL_2(O). For this, we determine, for arbitrary Dedekind…

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 primary-like submodules as a new generalization of graded primary ideals and give…

The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most…

Very flat and contradjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian…

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…