476.
The study of hyperidentities is a growing field of research. While hyperidentities hark back to before 1965 (cf. [1]), they
have found a rebirth in the late seventies and early eighties (cf. [8], [9]). It is being expanded in several directions,
from connections with clone theory, to finite basis problems, to semigroup theory, to classification of
M-solid varieties. Applications to digital logic, formal languages, and hypertext systems have been suggested. The concept
of a
P-compatible equation, where
P is a partition on the set of operation symbols, is a good tool to study the structure of identities. In [4] we asked for
P-compatible hyperidentities.
In this paper we will consider hypersubstitutions which are compatible with the partition
P and will develop a generalized equational theory for certain
P-compatible hyperidentities.
This revised version was published online in June 2006 with corrections to the Cover Date.
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