Zobrazeno 1 - 10
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pro vyhledávání: '"Coykendall, Jim"'
We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own factorization proper
Externí odkaz:
http://arxiv.org/abs/2406.14803
Autor:
Coykendall, Jim, Gotti, Felix
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and, therefore, divi
Externí odkaz:
http://arxiv.org/abs/2406.02503
Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if whenever $a^2 - b^2 \in I$ for $0 \neq a, b \in R$, then $a + b \in I$ or $a - b \in I$. In t
Externí odkaz:
http://arxiv.org/abs/2402.18704
Autor:
al-Kaseasbeh, Saba, Coykendall, Jim
In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph theoretic structure of the associa
Externí odkaz:
http://arxiv.org/abs/2303.00148
Autor:
Coykendall, Jim, Dutta, Tridib
The SFT (for strong finite type) condition was introduced by J. Arnold in the context of studying the condition for formal power series rings to have finite Krull dimension. In the context of commutative rings, the SFT property is a near-Noetherian p
Externí odkaz:
http://arxiv.org/abs/2301.01663
If every subring of an integral domain is atomic, then we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in t
Externí odkaz:
http://arxiv.org/abs/2112.00264
An atomic monoid $M$ is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element $x \in M$ no two distinct factorizations of $x$ have the same length. The notion of length-factoriality was introduced by
Externí odkaz:
http://arxiv.org/abs/2101.05441
Autor:
Coykendall, Jim, Gotti, Felix
Let $M$ be a commutative cancellative monoid, and let $R$ be an integral domain. The question of whether the monoid ring $R[x;M]$ is atomic provided that both $M$ and $R$ are atomic dates back to the 1980s. In 1993, Roitman gave a negative answer to
Externí odkaz:
http://arxiv.org/abs/1906.11138
Autor:
Coykendall, Jim, Trentham, Stacy
In this paper, we show that it is possible for a commutative ring with identity to be non-atomic (that is, there exist non-zero nonunits that cannot be factored into irreducibles) and yet have a strongly atomic polynomial extension. In particular, we
Externí odkaz:
http://arxiv.org/abs/1612.05976
Autor:
Boynton, Jason Greene, Coykendall, Jim
Publikováno v:
Can. Math. Bull. 58 (2015) 449-458
It is well-known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current understanding of facto
Externí odkaz:
http://arxiv.org/abs/1304.0063