Finite simple abelian algebras are strictly simple
نویسندگان
چکیده
منابع مشابه
Finite Simple Abelian Algebras Are Strictly Simple
A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x,y) and for all elements a, b, c, d, we have the following implication: t(a,c) = t(a,d) —> t(b,c) = t(b,d) . It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well-known fact about Abelia...
متن کاملFinite Simple Abelian Algebras
A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x, ȳ) and for all elements a, b, c̄, d̄, we have the following implication: t(a, c̄) = t(a, d̄) −→ t(b, c̄) = t(b, d̄). It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well known fact about Ab...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1990-0990434-2