Ideals of direct products of rings
Rings and Algebras
2019-01-21 v1
Abstract
It is known that an ideal of a direct product of commutative unitary rings is directly decomposable into ideals of the corresponding factors. We show that this does not hold in general for commutative rings and we find necessary and sufficient conditions for direct decomposability of ideals. For varieties of commutative rings we derive a Mal'cev type condition characterizing direct decomposability of ideals and we determine explicitly all varieties satisfying this condition.
Keywords
Cite
@article{arxiv.1901.06362,
title = {Ideals of direct products of rings},
author = {Ivan Chajda and Günther Eigenthaler and Helmut Länger},
journal= {arXiv preprint arXiv:1901.06362},
year = {2019}
}