Results 141 to 150 of about 4,265 (160)

All varieties of regular orthogroups

Semigroup Forum, 1985
An orthogroup is a union of groups in which the idempotents form a subsemigroup (orthodox union of groups). If in addition the idempotents form a regular band, the semigroup is a regular orthogroup. These semigroups form a variety when considered as semigroups with an inverse.
Mariio Petrich, Petrich Mario
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Global determinism of normal orthogroups

Semigroup Forum, 2016
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Xianzhong Zhao, Zhao Xianzhong
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PhyloMCL: Accurate clustering of hierarchical orthogroups guided by phylogenetic relationship and inference of polyploidy events

Methods in Ecology and Evolution, 2020
AbstractIdentification of homology relationships is essential for inferring gene functions, detecting phylogeny of gene families, discovering evolutionary history of life, and usually, is the first step of many genetic and genomic studies. However, the presence of gene duplicates, variation on evolutionary rates of homologs, fusion and fission of genes,
Ji Qi, Shengyu Zhou, Yamao Chen
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The Word Problem for Orthogroups

Canadian Journal of Mathematics, 1981
A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a-l for a ∈ S be the group inverse of a in the maximal ...
Gerhard, J. A., Petrich, Mario
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WLR-regular orthogroups

Semigroup Forum, 2008
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Zhang, Jiangang, Song, Guangtian, Liu, Guoxin   +2 more
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Hall-type representations for generalised orthogroups

Semigroup Forum, 2014
An orthodox semigroup is called orthogroup if it is completely regular. Let \(U\) be a subset of the set \(E(S)\) of all idempotents of a semigroup \(S\). Let \(a\widetilde{\mathcal L}_U b\) iff \((\forall e\in U)(ae=a\Leftrightarrow be=b)\). Dually, the relation \(\widetilde{\mathcal R}_U\) is defined. \(S\) is called weakly \(U\)-abundant if every \(\
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Radicals of semigroup rings of orthogroups

Semigroup Forum, 1990
Let S be an orthogroup, that is a completely regular semigroup the idempotent set of which is a subsemigroup. By a result of \textit{M. Petrich} [Proc. Am. Math. Soc. 99, 617-622 (1987; Zbl 0622.20050)], S is a semilattice Y of semigroups \(S_{\alpha}=I_{\alpha}\times G_{\alpha}\times \Lambda_{\alpha}\), \(\alpha\in Y\), where \(I_{\alpha ...
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Λ-Right congruences and a classification of orthogroups

Acta Mathematica Hungarica, 1984
The author defines a \(\wedge\)-right congruence on a completely regular semigroup S as any left congruence \(\rho\) on S for which (i) \(a\rho\) \(\hat a\) and (ii) \(a\rho\) b implies \(\hat ac\rho\) \^bc for any a,b,c in S. (Here \(\hat a\) denotes the unit of \(H_ a)\). The dual notion defines \(\wedge\)-left congruences.
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EXTENSIONS OF REGULAR ORTHOGROUPS BY INVERSE SEMIGROUPS

International Journal of Algebra and Computation, 1995
Let V be a variety of regular orthogroups, i.e. completely regular orthodox semigroups whose band of idempotents is regular. Let S be an orthodox semigroup which is a (normal) extension of an orthogroup K from V by an inverse semigroup G, that is, there is a congruence ρ on S such that the semigroup ker ρ of all idempotent related elements of S is ...
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Extensions of regular orthogroups by groups

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1995
AbstractA common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented.
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