FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 3, PAGES 183-203

A general version of standard bases in associative algebras and their universal constructions

V. N. Latyshev

Abstract

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This work is devoted, in some sense, to "methodical" questions. A general version of standard basis in ideal of algebra is presented which uses a notion of so called algebra with a strong filtration introduced recently by the author. Moreover, universal constructions related this class of algebras such as direct sums, tensor products, and free modules are considered.

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Last modified: January 13, 2010