Geodesic
On finiteness conditions for subalgebras with zero multiplication
Jan Krempa1
1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 123-135.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm102-1-11
Keywords: commutative ring unit paper associative f algebra study properties forced finite length dcc condition f submodules subalgebras zero multiplication conditions considered earlier either field ring rational integers final section consider algebras maximal commutative subalgebras finite length f modules obtain results parallel those known acc condition finite generation

Jan Krempa 1

1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Jan Krempa. On finiteness conditions for subalgebras with zero multiplication. Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 123-135. doi : 10.4064/cm102-1-11. http://geodesic.mathdoc.fr/articles/10.4064/cm102-1-11/

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