Let F be a commutative ring with unit. In this paper, for an associative F-algebra A we study some properties forced by finite length or DCC condition on F-submodules of A that are subalgebras with zero multiplication. Such conditions were considered earlier when F was either a field or the ring of rational integers. In the final section, we consider algebras with maximal commutative subalgebras of finite length as F-modules and obtain some results parallel to those known for ACC condition or finite generation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-11,
author = {Jan Krempa},
title = {On finiteness conditions for subalgebras with zero multiplication},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {123-135},
zbl = {1106.16022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-11}
}
Jan Krempa. On finiteness conditions for subalgebras with zero multiplication. Colloquium Mathematicae, Tome 103 (2005) pp. 123-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-11/