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

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)


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