Going Up and Lying Over in Congruence--modular Algebras
Rings and Algebras
2016-08-18 v1
Abstract
In this paper, we extend properties Going Up and Lying Over from ring theory to the general setting of congruence--modular equational classes, using the notion of prime congruence defined through the commutator. We show how these two properties relate to each other, prove that they are preserved by finite direct products and quotients and provide algebraic and topological characterizations for them. We also point out many kinds of varieties in which these properties always hold.
Keywords
Cite
@article{arxiv.1608.04985,
title = {Going Up and Lying Over in Congruence--modular Algebras},
author = {George Georgescu and Claudia Mureşan},
journal= {arXiv preprint arXiv:1608.04985},
year = {2016}
}
Comments
26 pages