A natural partial order for semigroups
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- by H. Mitsch
- Proc. Amer. Math. Soc. 97 (1986), 384-388
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840614-0
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Abstract:
A partial order on a semigroup $(S, \cdot )$ is called natural if it is defined by means of the multiplication of $S$. It is shown that for any semigroup $(S, \cdot )$ the relation $a \leq b$ iff $a = xb = by$, $xa = a$ for some $x$, $y \in {S^1}$, is a partial order. It coincides with the well-known natural partial order for regular semigroups defined by Hartwig [4] and Nambooripad [10]. Similar relations derived from the natural partial order on the regular semigroup $({T_X}, \circ )$ of all maps on the set $X$ are investigated.References
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Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 384-388
- MSC: Primary 20M10; Secondary 06F05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840614-0
- MathSciNet review: 840614