On finiteness conditions for subalgebras with zero multiplication

Tom 102 / 2005

Jan Krempa Colloquium Mathematicum 102 (2005), 123-135 MSC: 16N40, 16P70. DOI: 10.4064/cm102-1-11

Streszczenie

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.

Autorzy

  • Jan KrempaInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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