A universal algebra is simple if and only if it has more than one element and there are no proper homomorphisms defined upon it. In this note we study a related notion : an algebra is pseudo-simple if and only if it has more than one element and is isomorphic to all its proper (i.e., non-one-element) homomorphic images. The two concepts simplicity and pseudo-simplicity are examples of concepts ...

According to the number of sub-SL(8)s (sub-STS(7)s), there are five classes of sloops SL(16)s (STS(15)s) [2, 5].) In [4] the author has classified SL(20)s into 11 classes. Using computer technique in [10] the authors gave a large number for each class of SL(20)s. There are only simple SL(22)s and simple SL(26)s. So the next admissible cardinality is 28. Also, all SL(32)s are classified into 14 ...

First order theories for which the truth of a universal sentence on their finite models implies the truth on all models are investigated. It is proved that an equational theory has such a property if and only if every finitely presented model is residually finite. The most common classes of algebraic structures are discussed. 0. Introduction. John T. Baldwin in a review of the book Selected pap...

A group is ^-separating if a Boolean power of the group has a unique Boolean algebra. It is proved that a finite subdirectly irreducible group is S-separating if and only if it is non-Abelian. Suppose B is a Boolean ring and G is a group. Let B[G] denote the group ring of G with coefficient ring B. The Boolean power G [B] is defined to be the set of those elements 2e,.g,. EB[G] such that (1) 2e...

A group is subdirectly reducible if it has two non-trivial normal subgroups with trivial intersection. Such groups may be an easy case in certain inductive arguments. We prove that every solvable finite group can be generated by at most one subdirectly reducible subgroup together with two subgroups of prime-power order and one element. We also prove that every group of prime-power order can be ...

Abstract This is the second of a series papers that investigate fragments quasi-Nelson logic (QNL) from an algebraic standpoint. QNL, recently introduced as common generalization intuitionistic and Nelson’s constructive with strong negation, axiomatic extension substructural $FL_{ew}$ (full Lambek calculus exchange weakening) by Nelson axiom. The counterpart QNL (quasi-Nelson algebras) class co...

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

In that paper we study atoms of congruence lattices and subdirectly irreducibility algebras with one operator the main symmetric operation. A ternary operation

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...