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Reports on Mathematical Logic

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No. 31

Tomasz A. GORAZD,

The isomorphism testing for directly representable varieties
A b s t r a c t.
Let $\cal V$ be a variety of algebras with a finite list of finite directly
indecomposable members. We show that there is a polynomial time algorithm
that tests the isomorphism between any two finite algebras from $\cal V.$
This includes the following classical structures in algebra:

Abelian groups with $nx=0$, $n>0$,

Boolean algebras,

Rings with $x^m=x$, $m>1$,

Modules over a finite semisimple ring.

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