All idempotent and regular elements in the monoid of generalized hypersubstitutions for algebraic systems of type (2; 2)

Abstract

There are two different concepts for hypersubstitutions for algebraic systems [K. Denecke and D. Phusanga, Hyperformulas and solid algebraic systems, Studia Logica 90(2) (2008) 263–286; J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. In this paper, we follow the more natural and practicable one given in [J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. On the other hand, in [S. Leeratanavalee and K. Denecke, Generalized hypersubstitutions and strongly solid varieties, General Algebra and Applications, Proc. of 59th Workshop on General Algebra; 15th Conf. for Young Algebraists Potsdam 2000 (Shaker Verlag, 2000), pp. 135–145], the concept of the monoid of generalized hypersubstitutions was introduced. Following both ideas, one obtains the concept of a monoid of generalized hypersubstitutions for algebraic systems in a canonical way. The purpose of this paper is the study of the monoid of generalized hypersubstitutions for algebraic systems. We characterize the idempotent as well as regular elements in this monoid.