On the Equational Artinian Algebras
Group Theory
2015-06-18 v2 Logic
Abstract
Equational Artinian algebras were introduced in our previous work: {\em Equational conditions in universal algebraic geometry, to appear in Algebra and Logic, 2015}. In this note, we define the notion of {\em radical topology with respect to an algebra } and using the well-known K\"onig lemma in graph theory, we show that the algebra is equational Artinian iff this topology is noetherian. This completes the analogy between equational noetherian and equational Artinian algebras.
Cite
@article{arxiv.1506.00090,
title = {On the Equational Artinian Algebras},
author = {P. Modabberi and M. Shahryari},
journal= {arXiv preprint arXiv:1506.00090},
year = {2015}
}
Comments
10 pages, a theorem on ultrapowers is added. arXiv admin note: substantial text overlap with arXiv:1401.4389