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Natural partial order induced by a commutative, associative and idempotent function
Information Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrea Zemankova
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A natural partial order on certain semigroups of transformations with restricted range
Semigroup Forum, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun, Lei, Sun, Junling
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A Natural Partial Order on Partition Order-Decreasing Transformation Semigroups
Bulletin of the Iranian Mathematical Society, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Natural Partial Order on Certain Semigroups of Transformations Restricted by an Equivalence
Bulletin of the Iranian Mathematical Society, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, X., Sun, L.
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Semigroup Forum, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yanisa Chaiya
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yanisa Chaiya
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Semigroup Forum
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jintana Sanwong +2 more
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Jintana Sanwong +2 more
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The natural partial order on semirings
Lecture Notes in Mathematics, 1981John Zeleznikow
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Canadian Journal of Mathematics, 1968
Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering.
Dean, R. A., Keller, G.
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Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering.
Dean, R. A., Keller, G.
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THE NATURAL PARTIAL ORDER ON SOME TRANSFORMATION SEMIGROUPS
Bulletin of the Australian Mathematical Society, 2013AbstractFor a semigroup $S$, let ${S}^{1} $ be the semigroup obtained from $S$ by adding a new symbol 1 as its identity if $S$ has no identity; otherwise let ${S}^{1} = S$. Mitsch defined the natural partial order $\leqslant $ on a semigroup $S$ as follows: for $a, b\in S$, $a\leqslant b$ if and only if $a= xb= by$ and $a= ay$ for some $x, y\in {S}^{1}
Chaopraknoi, Sureeporn +2 more
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