On finiteness conditions for subalgebras with zero multiplication

Jan Krempa. "On finiteness conditions for subalgebras with zero multiplication." Colloquium Mathematicae 102.1 (2005): 123-135. <http://eudml.org/doc/284192>.

@article{JanKrempa2005,
abstract = {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.},
author = {Jan Krempa},
journal = {Colloquium Mathematicae},
keywords = {zero-subalgebras; finiteness conditions on submodules; -algebras; -algebras; modules of finite length; semiprime algebras; nilpotent elements; orthogonal idempotents; commutative subalgebras},
language = {eng},
number = {1},
pages = {123-135},
title = {On finiteness conditions for subalgebras with zero multiplication},
url = {http://eudml.org/doc/284192},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Jan Krempa
TI - On finiteness conditions for subalgebras with zero multiplication
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 123
EP - 135
AB - 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.
LA - eng
KW - zero-subalgebras; finiteness conditions on submodules; -algebras; -algebras; modules of finite length; semiprime algebras; nilpotent elements; orthogonal idempotents; commutative subalgebras
UR - http://eudml.org/doc/284192
ER -