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On hierarchical competition through reduction of individual growth. [PDF]

open access: yesJ Math Biol
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SEMIGROUPS WITH INVERSE TRANSVERSALS AS MATRIX SEMIGROUPS

The Quarterly Journal of Mathematics, 1984
Let S be a regular semigroup. An inverse subsemigroup \(S^ 0\) of S is called an inverse transversal for S if \(S^ 0=S^ 0SS^ 0\) and each \(a\in S\) has a unique inverse \(a^ 0\in S^ 0\). We shall only speak about regular semigroups containing an inverse transversal. In a recent paper [ibid.
McAlister, D. B., McFadden, R. B.
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Semigroups of inverse quotients

Periodica Mathematica Hungarica, 2012
The paper discusses the notion of left I-quotients in inverse semigroups. A subsemigroup \(S\) of an inverse semigroup \(Q\) is called a left I-order in \(Q\) (and \(Q\) is a semigroup of left I-quotients of \(S\)) if every \(q\in Q\) can be written as \(q=a^{-1}b\) where \(a,b\in S\).
Nassraddin Ghroda, Victoria Gould
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On Finite Semigroups Embeddable in Inverse Semigroups

Semigroup Forum, 2001
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