Gaussian trivial ring extensions and fqp-rings
Rings and Algebras
2015-07-09 v1 Commutative Algebra
Abstract
Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be B{\'e}zout is also studied, but a response is only given in the case where pSpec A (a quotient space of Spec} A) is totally disconnected. Trivial ring extensions which are fqp-rings are characterized only in the local case. To get a general result we intoduce the class of fqf-rings satisfying a weaker property than fqp-ring. Moreover, it is proven that the finitistic weak dimension of a fqf-ring is 0, 1 or 2 and its global weak dimension is 0, 1 or infinite.
Keywords
Cite
@article{arxiv.1507.02248,
title = {Gaussian trivial ring extensions and fqp-rings},
author = {Francois Couchot},
journal= {arXiv preprint arXiv:1507.02248},
year = {2015}
}