相关论文: Associativity and Commutativity of Partially Order…

We give axioms in the language of rings augmented by a 1-ary predicate symbol $Fin(x)$ with intended interpretation in the Boolean algebra of idempotents as the ideal of finite elements, i.e. finite unions of atoms. We prove that any…

Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…

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…

This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming…

Categorical models of the exponential modality of linear logic will often, but not always, support an operation of differentiation. When they do, we speak of a monoidal differential modality; when they do not, we have merely a monoidal…

Let $R$ be a commutative ring with identity and $T(R)$ its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to…

We study enumeration problems for multi-operator monomials generated from one indeterminate by an associative multiplication together with finitely many unary operators. We consider four regimes, according to whether multiplication is…

We introduce ($\ell$-)bimonoids as ordered algebras consisting of two compatible monoidal structures on a partially ordered (lattice-ordered) set. Bimonoids form an appropriate framework for the study of a general notion of complementation,…

Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that…

A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $\alpha$, the additive monoid $M_\alpha$ of the evaluation semiring…

In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup $S$ we have $x^p y^p = y^p x^p$ and $x^q y^q = y^q x^q$ for all $x,y\in S$ where…

Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild…

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…

Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…

The usual coherence theorem of MacLane for categories with multiplication assumes that a certain pentagonal diagram commutes in order to conclude that associativity isomorphisms are well defined in a certain practical sense. The practical…

$(1)$ Let $M\subset N$ be a commutative cancellative torsion-free and subintegral extension of monoids. Then we prove that in the case of ring extension $A[M]\subset A[N]$, the two notions, subintegral and weakly subintegral coincide…

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…

Let $\mu$ be a $K$-invariant compactly supported distribution on a noncompact Riemannian symmetric space $X=G/K$. If the spherical Fourier transform $\widetilde\mu(\lambda)$ is slowly decreasing, it is known that the right convolution…

We study a nonlinear analogue of additive commutators, known as \textit{polynomial commutators}, defined by $p(ab) - p(ba)$ for a polynomial $p \in F[x]$ and elements $a, b$ in an algebra $R$ over a field $F$. Originally introduced by…

Let $F$ be a field and let $F \langle X \rangle$ be the free unital associative algebra over $F$ freely generated by an infinite countable set $X = \{x_1, x_2, \dots \}$. Define a left-normed commutator $[a_1, a_2, \dots, a_n]$ recursively…