Results 31 to 40 of about 234,678 (87)

On quasi-Pr\"{u}fer and UM$t$ domains [PDF]

, 2011
In this note we show that an integral domain $D$ of finite $w$-dimension is a quasi-Pr\"{u}fer domain if and only if each overring of $D$ is a $w$-Jaffard domain.
Sahandi, Parviz
core  

On monogenic functions defined in different commutative algebras [PDF]

arXiv, 2018
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
arxiv  

Idempotents and zero divisors in commutative algebras satisfying an identity of degree four

International Electronic Journal of Algebra
We study commutative algebras satisfying the identity $ ((wx)y)z+((wy)z)x+((wz)x)y-((wy)x)z- ((wx)z)y-((wz)y)x = 0. $ We assume characteristic of the field $\neq 2,3.$ We prove that given any $\lambda \in F,$ there exists a commutative algebra with ...
Manuel Arenas, Iván Correa, I. Hentzel, Alicia Labra   +3 more
semanticscholar   +1 more source

Homogeneous Buchberger algorithms and Sullivant's computational commutative algebra challenge [PDF]

arXiv, 2005
We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge.
arxiv  

$n$-strongly Gorenstein rings [PDF]

arXiv, 2011
This paper introduces and studies a particular subclass of the class of commutative rings with finite Gorenstein global dimension.
arxiv  

The Snake Lemma [PDF]

arXiv, 2011
We present a rather general version of the snake lemma for abelian groups.
arxiv  

Frobenius Splitting in Commutative Algebra [PDF]

arXiv, 2014
This is a survey of Frobenius splitting techniques in commutative algebra, based on the first author's lectures at the introductory workshop for the special year in commutative algebra at MSRI in fall 2012.
arxiv  

Homotopical Aspects of Commutative Algebras I: Freeness Conditions for Crossed Squares [PDF]

arXiv, 2009
We give an alternative description of the top algebra of the free crossed square of algebras on 2-construction data in terms of tensors and coproducts of crossed modules of commutative algebras.
arxiv  

Simple graded commutative algebras [PDF]

arXiv, 2009
We study the notion of $\Gamma$-graded commutative algebra for an arbitrary abelian group $\Gamma$. The main examples are the Clifford algebras already treated by Albuquerque and Majid. We prove that the Clifford algebras are the only simple finite-dimensional associative graded commutative algebras over $\mathbb{R}$ or $\mathbb{C}$.
arxiv  

Lying-Over Theorem on Left Commutative Rngs [PDF]

arXiv, 2005
We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings.
arxiv