Results 1 to 10 of about 37 (22)

On Orders in Normal Cryptogroups [PDF]

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   +8 more sources

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

A Construction of Regular Cryptogroups

Semigroup Forum, 2004
A semigroup \(S\) is called a cryptogroup if Green's relation \(\mathcal H\) is a congruence of \(S\). If \(S/\mathcal H\) is a regular band (a band is regular if it satisfies the identity \(xyzx=xyxzx\)) then \(S\) is a regular cryptogroup. A description of regular cryptogroups by a left regular band and a right regular band with the same structural ...
Song, Guangtian, Liu, Guoxin, Zhang, Jiangang   +2 more
exaly   +3 more sources

A Construction of Cryptogroups

Acta Mathematica Sinica, English Series, 2006
A completely regular semigroup \(S\) is called a cryptogroup if Green's relation \(\mathcal H\) on \(S\) is a congruence. It was proved [by \textit{M. Petrich} and \textit{N. R. Reilly}, Completely regular semigroups. Wiley (1999; Zbl 0967.20034)] that a completely regular semigroup \(S\) is a normal cryptogroup iff \(S\) is a strong semilattice of ...
Song, Guangtian, Liu, Guoxin, Zhang, Jiangang   +2 more
exaly   +2 more sources

On the Structure of Cryptogroups

Semigroup Forum, 2006
In this paper, we give a structure theorem for cryptogroups by means of bands and homomorphisms between completely simple semigroups.
Guangtian Song, Xiangqin Meng, Guoxin Liu   +2 more
exaly   +2 more sources

A Problem on Central Cryptogroups

Semigroup Forum, 2006
A completely regular semigroup \(S\) is called `central' if the product of any two idempotents of \(S\) lies in the center of the maximal subgroup containing it; if the Green relation \(\mathcal H\) is a congruence on \(S\), then \(S\) is called a `cryptogroup'. The classes of all cryptogroups, central cryptogroups and orthodox cryptogroups are denoted
Liu, Guoxin, Zhang, Jiangang
exaly   +3 more sources

Cryptogroups with an associate subgroup

Acta Mathematica Hungarica, 2013
A cryptogroup is a completely regular semigroup \(S\) on which Green's relation \(\mathcal H\) is a congruence. \(S\) is called overabelian if all subgroups of \(S\) are Abelian. A subgroup \(G\) of \(S\) is associate subgroup of \(S\) if for each \(a\in S\) there exists exactly one \(x\in G\) such that \(a=axa\).
Mariio Petrich, Petrich Mario
exaly   +2 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

TK -operator Semigroups for Cryptogroups

Semigroup Forum, 2000
A by now standard way of studying the lattice of congruences on a regular semigroup is via the trace and kernel operators: with any congruence \(\rho\) are associated \(\rho k\), \(\rho K\), \(\rho t\), \(\rho T\), respectively the least and greatest congruences with the same kernel (union of idempotent classes) as \(\rho\), and the least and greatest ...
exaly   +3 more sources

The Refined Semilattice Construction Of Locally Orthodox Regular Cryptogroups

Communications in Algebra, 2012
In this article, we show that a semigroup is a locally orthodox regular cryptogroup if and only if it is isomorphic to a refined semilattice of completely simple semigroups. This structural description is specialized to left (respectively, right) quasinormal cryptogroups. The strong semilattice construction of normal cryptogroups is also a special case.
Houyi Yu, Zhengpan Wang
exaly   +2 more sources