Zobrazeno 1 - 10
of 1 233
pro vyhledávání: '"13A15"'
Autor:
Nasehpour, Peyman
In this paper, we prove prime avoidance for ringoids. We also generalize McCoy's and Davis' prime avoidance theorems in the context of semiring theory. Next, we proceed to define and characterize compactly packed semirings and show that a commutative
Externí odkaz:
http://arxiv.org/abs/2411.10725
Autor:
Guerrieri, Lorenzo
Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$ nonzero element
Externí odkaz:
http://arxiv.org/abs/2411.00616
Let $R$ be a commutative ring with unity and let $X$ be an indeterminate over $R$. The \textit{Anderson ring} of $R$ is defined as the quotient ring of the polynomial ring $R[X]$ by the set of polynomials that evaluate to $1$ at $0$. Specifically, th
Externí odkaz:
http://arxiv.org/abs/2410.17007
Autor:
Chang, Gyu Whan, Reinhart, Andreas
An integral domain $D$ is a valuation ideal factorization domain (VIFD) if each nonzero principal ideal of $D$ can be written as a finite product of valuation ideals. Clearly, $\pi$-domains are VIFDs. In this paper, we study the ring-theoretic proper
Externí odkaz:
http://arxiv.org/abs/2410.16471
Autor:
Yiğit, Uğur, Koç, Suat
Let $R\ $be an integral domain and $R^{\#}$ the set of all nonzero nonunits of $R.\ $For every elements $a,b\in R^{\#},$ we define $a\sim b$ if and only if $aR=bR,$ that is, $a$ and $b$ are associated elements. Suppose that $EC(R^{\#})$ is the set of
Externí odkaz:
http://arxiv.org/abs/2409.10577
Autor:
Tarizadeh, Abolfazl
An important classical result in ZFC asserts that every infinite cardinal number is idempotent. Using this fact, we obtain several algebraic results in this article. The first result asserts that an infinite Abelian group has a proper subgroup with t
Externí odkaz:
http://arxiv.org/abs/2409.02488
Autor:
Baek, Hyungtae, Lim, Jung Wook
Many ring theorists researched various properties of Nagata rings and Serre's conjecture rings. In this paper, we introduce a subring (refer to the Anderson ring) of both the Nagata ring and the Serre's conjecture ring (up to isomorphism), and invest
Externí odkaz:
http://arxiv.org/abs/2408.08758
Autor:
Abedi, Mostafa
Consider the subring $\mathcal{R}_cL$ of continuous real-valued functions defined on a frame $L$, comprising functions with a countable pointfree image. We present some useful properties of $\mathcal{R}_cL$. We establish that both $\mathcal{R}_cL$ an
Externí odkaz:
http://arxiv.org/abs/2408.05473
Autor:
Reinhart, Andreas, Ulucak, Gulsen
In [22], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime elements in C-lattices. We investigate the C-lattices in which every el
Externí odkaz:
http://arxiv.org/abs/2408.01100
In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theorems on (left) Artinian rings and modules, due to Akizuki, Anderson, Hop
Externí odkaz:
http://arxiv.org/abs/2407.20488