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P-Compatible Hypersubstitution and MP-Solid Varieties

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Abstract

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.

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HŁkowska, K., Denecke, K. P-Compatible Hypersubstitution and MP-Solid Varieties. Studia Logica 64, 355–363 (2000). https://doi.org/10.1023/A:1005241711448

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  • DOI: https://doi.org/10.1023/A:1005241711448

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