Semiprimality relative to *-congruences
by
Marcel Tonga
Dept. of Maths. ; Faculty of Science; University of Yaoundé-1 (Cameroon)
Coauthors: Etienne R. Temgoua Alomo

A finite non trivial algebra B is called semiprimal if it is quasiprimal and any isomorphism between two non trivial (not necessarily distinct) subalgebras of B is the identity. For a fisrt order structure D, a congruence O of D is called a *-congruence if O is compatible with the relations of D. When O is different from the identity of D and from DxD, the underlying algebra of D is not quasiprimal. We formulate and characterize a notion of semiprimality for such first order structure, which reduces to the classical case of algebras when D has no relation.

Date received: May 21, 2004