Related papers: Rings with common division, common meadows and the…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
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…
The following representation theorem is proven: A partially ordered commutative ring $R$ is a subring of a ring of almost everywhere defined continuous real-valued functions on a compact Hausdorff space $X$ if and only if $R$ is archimedean…
In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
When a semigroup has a unary operation, it is possible to define two binary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to…
Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
In this paper, we have studied the axiomatics of {\it Ann-categories} and {\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have…
We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…
This article studies the equation $[A,B]^k = {\rm Id}_n$ for matrices over $\mathbb{C}$, characterizing the pairs $(k,n)$ for which solutions exist via a classical result of Lam and Leung on sums of roots of unity. The problem is next…
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…
This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3…
Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
For a multiplicative cohomology theory E, complex orientations are in bijective correspondence with multiplicative natural transformations to E from complex bordism cohomology MU. If E is represented by a spectrum with a highly structured…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
A classical theorem by Jacobson says that a ring in which every element $x$ satisfies the equation $x^n=x$ for some $n>1$ is commutative. According to Birkhoff's Completeness Theorem, if $n$ is fixed, there must be an equational proof of…
For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are…
A well-known result of K\"{o}the and Cohen-Kaplansky states that a commutative ring $R$ has the property that every $R$-module is a direct sum of cyclic modules if and only if $R$ is an Artinian principal ideal ring. This motivated us to…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…