P-Compatible Hypersubstitution and MP-Solid Varieties |
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Authors: | HŁkowska K. Denecke K. |
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Affiliation: | (1) Institute of Mathematics, University of Opole, ul. Oleska 48, Opole, Poland;(2) Institute of Mathematics, University of Potsdam, Am Neuen Palais, 14415 Potsdam, Germany |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | P-compatible identities P-compatible hypersubstitutions |
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