The spectrum of the variety of anti-rectangular Abel Grassmann bands

Details The spectrum of the variety of anti-rectangular Abel Grassmann bands The spectrum of the variety of anti-rectangular Abel Grassmann bands

2011-02-08

arxiv.org/abs/1102.1637v1

Mathematics

Rings and Algebras

Scientific paper

We prove that the set of all orders of finite algebras in the groupoid variety of anti-rectangular Abel Grassmann bands consists of all powers of four. We also prove that any groupoid anti-isomorphic to a finite or countable anti-rectangular Abel Grassmann band G is isomorphic to G. It is proved that within isomorphism there is only one countable anti-rectangular Abel Grassmann band and that it is isomophic to a proper subgroupoid of itself.

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