Some varieties containing relation algebras

Author:
Roger Maddux

Journal:
Trans. Amer. Math. Soc. **272** (1982), 501-526

MSC:
Primary 03G15; Secondary 03G25, 06E99, 08C10

MathSciNet review:
662049

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Abstract: Three varieties of algebras are introduced which extend the variety of relation algebras. They are obtained from by weakening the associative law for relative product, and are consequently called nonassociative, weakly-associative and semiassociative relation algebras, or , , and , respectively. Each of these varieties arises naturally in solving various problems concerning relation algebras. We show, for example, that is the only one of these varieties which is closed under the formation of complex algebras of atom structures of algebras, and that is the closure of the variety of representable 's under relativization. The paper also contains a study of the elementary theories of these varieties, various representation theorems, and numerous examples.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0662049-7

Keywords:
Relation algebra,
Boolean algebra with operators,
relativization,
complex algebra

Article copyright:
© Copyright 1982
American Mathematical Society