On finiteness conditions for subalgebras with zero multiplication

• Autorzy: Jan Krempa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16P70: Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
• 16N40: Nil and nilpotent radicals, sets, ideals, rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 1
• Strony: 123-135

Daty

wydano

2005

Twórcy

autor

Jan Krempa

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm102-1-11