Results 1 to 10 of about 28 (22)

Normal cryptogroups with an associate subgroup [PDF]

Czechoslovak Mathematical Journal, 2013
A subgroup \(G\) of a semigroup \(S\) is called an associate subgroup of \(S\) if for every \(s\in S\) there exists exactly one \(g\in G\) such that \(sgs=s\). In a previous paper [Publ. Math. 73, No. 3-4, 281-298 (2008; Zbl 1181.20051)] the author characterized all normal bands of groups (or equivalently, strong semilattices of completely simple ...
Petrich Mario
exaly   +3 more sources

On Orders in Normal Cryptogroups

Results in Mathematics, 2011
Given a semigroup \(Q\), a subsemigroup \(S\) of \(Q\) is said to be an \textit{order} in \(Q\) if every element of \(Q\) is a ``quotient'' of elements of \(S\), i.e., for all \(q\in Q\) there exist \(a,b,c,d\in S\) such that \(a\) and \(d\) belong to (maximal) subgroups of \(Q\) and \(q=a^{-1}b=cd^{-1}\), where \(a^{-1}\) and \(d^{-1}\) are the ...
Petrich Mario
exaly   +6 more sources

WLR-Normal Cryptogroups and LR-Regular Semigroups

Lecture Notes in Electrical Engineering, 2011
In this paper, we define the WLR-normal band, WLR-normal cryptogroup and LR-regular semigroup. We give some equivalent conditions for a completely regular semigroup to be a WLR-normal cryptogroup and give the characterization of LR-regular semigroups.
Aifa Wang, Lili Wang, Yinbin Li
exaly   +2 more sources

The existence of an associate subgroup in normal cryptogroups

Publicationes Mathematicae, 2008
Let \(S\) be a semigroup. If \(a=axa\) for \(a,x\in A\) then \(x\) is called an associate of \(a\). A subgroup \(G\) of \(S\) is an associate subgroup of \(S\) if it contains exactly one associate of each element of \(S\). Every maximal subgroup of a regular semigroup \(S\) is an associate subgroup if and only if \(S\) is completely simple, or ...
exaly   +2 more sources

GREEN ♯-RELATIONS AND NORMAL ${\cal H}^\sharp$-CRYPTOGROUPS

Asian-European Journal of Mathematics, 2009
In this paper, a new set of generalized Green's relations on a semigroup S, namely the set of Green ♯-relations, are introduced. By using these new Green ♯-relations, we prove that an [Formula: see text]-abundant semigroup is a normal [Formula: see text]-cryptogroup if and only if it is a strong semilattice of completely [Formula: see text]-simple ...
Xiang-zhi Kong, K. P. Shum
openaire   +1 more source

Some Normal Cryptogroups as Semigroups of Isomorphisms

Results in Mathematics, 1996
A cryptogroup \(S\) is a completely regular semigroup in which the Green relation \(\mathcal H\) is a congruence, that is a band of groups. If, in addition, \(S/{\mathcal H}\) is a normal band, then \(S\) is a normal cryptogroup or a normal band of groups. A semilattice of groups \(G=[Y;G_\alpha,w_{\alpha,\beta}]\) is called a Clifford semigroup. Given
openaire   +2 more sources

Basis reduction for cryptogroups and orthogroups

Semigroup Forum, 2020
A C Casimiro, Eduardo Skapinakis
exaly  

On Malcev Products of Normal Cryptogroups

Results in Mathematics, 2014
Mariio Petrich, Petrich Mario
exaly  

A Lattice of Quasivarieties of Normal Cryptogroups

Semigroup Forum, 2007
Mariio Petrich, Petrich Mario
exaly  

Cryptogroups with an associate subgroup

Acta Mathematica Hungarica, 2013
Mariio Petrich, Petrich Mario
exaly