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Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two.
- Source :
-
Mathematical Notes . Sep/Oct2003, Vol. 74 Issue 3/4, p569-577. 9p. - Publication Year :
- 2003
-
Abstract
- Let <MATH>\frak B</MATH> (<MATH>\frak D</MATH>) be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity <MATH>((((x_1,x_2),x_3), ((x_4,x_5),x_6)),</MATH><MATH>(x_7,x_8))=\nomathbreak 0</MATH> (<MATH>((x_1x_2\cdot x_3)(x_4x_5\cdot x_6))(x_7x_8)=\nomathbreak 0</MATH>, respectively). In this paper, we construct infinite independent systems of identities in the variety <MATH>\frak B</MATH> (<MATH>\frak D</MATH>, respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety <MATH>\frak B</MATH> (<MATH>\frak D</MATH>) has the cardinality of the continuum and that there are algebras in <MATH>\frak B</MATH> (<MATH>\frak D</MATH>) with undecidable word problem. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*INFINITY (Mathematics)
*ARITHMETIC
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 74
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 16822925
- Full Text :
- https://doi.org/10.1023/A:1026156113443