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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Epimorphically closed permutative varieties


Author: N. M. Khan
Journal: Trans. Amer. Math. Soc. 287 (1985), 507-528
MSC: Primary 20M07
DOI: https://doi.org/10.1090/S0002-9947-1985-0768723-9
MathSciNet review: 768723
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Abstract: We show that for semigroups all permutation identities are preserved under epis and that all subvarieties of the permutative variety defined by any permutation identity

$\displaystyle {x_1}{x_2} \cdots {x_n} = {x_{{i_1}}}{x_{{i_2}}} \cdots {x_{{i_n}}},$

with $ n \geqslant 3$ and such that $ {i_n} \ne n$ or $ {i_1} \ne 1$, are closed under epis. Finally we find some sufficient conditions that an identity be preserved under epis in conjunction with any nontrivial permutation identity.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0768723-9
Keywords: Semigroup, variety, epimorphism, dominion
Article copyright: © Copyright 1985 American Mathematical Society