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- W1984663528 abstract "ABSTRACT Let S be a regular semigroup with set of idempotents E(S). We say that S is pure if, for all E(S) and , in the natural order implies that . We study the influence of purity on various constructions which produce semigroups belonging to some familiar classes of regular semigroups as well as examine the relationship of purity and -unitariness. This condition appears most natural on locally inverse semigroups where it is equivalent to the greatest idempotent pure congruence being a completely simple congruence. We also construct a relatively free completely regular semigroup generated by where and apply this result to obtain a criterion for purity for completely regular semigroups." @default.
- W1984663528 created "2016-06-24" @default.
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- W1984663528 date "2002-02-25" @default.
- W1984663528 modified "2023-10-17" @default.
- W1984663528 title "A CONDITION ON THE NATURAL ORDER FOR REGULAR SEMIGROUPS" @default.
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- W1984663528 doi "https://doi.org/10.1081/agb-120013167" @default.
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