Complete permutability of partitions in a set. I. (English) Zbl 0728.08001

Ševečková, Jitka; Šik, František

Arch. Math., Brno 25, No. 1-2, 95-102 (1989).

The notion of complete permutability of partitions has been introduced by Hashimoto in order to characterize direct product constructions. This paper gives a generalization of this notion to a family of partitions on subsets of a given set together with some characterizations for such families of partitions. For applications of these characterizations the reader is referred to a forthcoming part II of the paper.

Reviewer: H.Werner (Kassel)

MSC:

08A02	Relational systems, laws of composition
03E20	Other classical set theory (including functions, relations, and set algebra)
08A30	Subalgebras, congruence relations
06F15	Ordered groups

Keywords:

associability; complete permutability of partitions