Throughout this paper, all groups are finite. A group class closed under taking homomorphic images and finite subdirect products is called a formation . The symbol σ denotes some partition of the set primes. V. G. Safonov, I. N. Safonova, A. Skiba (Commun. Algebra. 2020. Vol. 48, № 9. P. 4002–4012) defined generalized σ-function. Any function f form : È {Ø} → {formations groups}, where (Ø) ≠ ∅,...

Abstract. In order to study the axiomatization of the if-then-else construct over possibly non-halting programs and tests, this paper introduces the notion of C-sets by considering the tests from an abstract C-algebra. When the C-algebra is an ada, the axiomatization is shown to be complete by obtaining a subdirect representation of C-sets. Further, this paper considers the equality test with t...

We bring together algebraic concepts such as equational class and various concepts from graph theory for developing a structure theory for graphs that promotes a deeper analysis of their metric properties. The basic operators are Cartesian multiplication and gated amalgamation or, alternatively, retraction. Specifically, finite weakly median graphs are known to be decomposable (relative to thes...

BL-algebras are the Lindembaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear)BLalgebras. A local BL-algebra is either locally finite (and hence an MValgebra) or perfect or peculiar. Here we study extensively perfect BLalgebras characterizing, with a finite sch...

A class K of similar algebras is said to have the finite embeddability property (briefly, the FEP) if every finite subset of an algebra in K can be extended to a finite algebra in K, with preservation of all partial operations. If a finitely axiomatized variety or quasivariety of finite type has the FEP, then its universal first order theory is decidable, hence its equational and quasi-equation...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...