Simple surjective algebras having no proper subalgebras

Journal of the Australian Mathematical Society

Ágnes Szendrei¹ 

关键词: 08 A 05;    08 A 40;    08 B 05;   

DOI  :  10.1017/S1446788700029979

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.

【 授权许可】

Unknown