Minimal Formations of Universal Algebras
نویسندگان
چکیده
A class F of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ F is in F ; 2) If α1, α2 are congruences on A and A/αi ∈ F , i = 1, 2, then A/(α1∩ α2) ∈ F . We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba on formations of finite universal algebras proposed in 1989.
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