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A Generalization of Fregular Semigroups
"... A regular semigroup S is termed locally Fregular, if each class of the least completely simple congruence ξ contains a greatest element with respect to the natural partial order. It is shown that each locally Fregular semigroup S admits an embedding into a semidirect product of a band by S/ξ. Furt ..."
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A regular semigroup S is termed locally Fregular, if each class of the least completely simple congruence ξ contains a greatest element with respect to the natural partial order. It is shown that each locally Fregular semigroup S admits an embedding into a semidirect product of a band by S
Surjectivity of multiplication and Fregularity of multigraded rings
"... this paper is to study this property, mainly for normal domains. After that, we show that surjectively graded normal domains in positive characteristic behaves well with respect to strong F regularity, utilizing the notion of global F regularity defined and studied by Smith [17]. This approach giv ..."
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Cited by 2 (1 self)
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this paper is to study this property, mainly for normal domains. After that, we show that surjectively graded normal domains in positive characteristic behaves well with respect to strong F regularity, utilizing the notion of global F regularity defined and studied by Smith [17]. This approach
ON TRANSFORMATION SEMIGROUPS WHICH ARE SEMIGROUPS
, 2006
"... A semigroup whose biideals and quasiideals coincide is called a semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular semig ..."
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A semigroup whose biideals and quasiideals coincide is called a semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular
Periodic Functions for Finite Semigroups
, 1998
"... . This paper introduces the concept of ultimately periodic functions for finite semigroups. Ultimately periodic functions are shown to be the same as regularitypreserving functions in automata theory. This characterization reveals the true algebraic nature of regularitypreserving functions. It mak ..."
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Cited by 3 (0 self)
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is motivated from the study of regularitypreserving functions in formal language theory (Zhang [12]). It is selfevident that this concept is of independent mathematical interest as well. A function f : IN ! IN on nonnegative integers is called ultimately periodic with respect to finite semigroups if for any
Semidirect Products of Regular Semigroups
 Trans. Amer. Math. Soc
, 1999
"... Within the usual semidirect product S T of regular semigroups S and T lies the set Reg (S T ) of its regular elements. Whenever S or T is completely simple, Reg (S T ) is a (regular) subsemigroup. It is this `product' that is the theme of the paper. It is best studied within the framework ..."
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Cited by 4 (4 self)
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the framework of existence (or e) varieties of regular semigroups. Given two such classes, U and V , the evariety U V generated by fReg (S T ) : S 2 U; T 2 V g, is well defined if and only if either U or V is contained within the evariety CS of completely simple semigroups. General properties
The Class of Structurally Regular Semigroups
, 2005
"... A semigroup S is said to be structurally regular if there exists an ordered pair (n; m) of nonnegative integers such that the quotient S=(n; m) is regular in the usual sense. The congruence (n; m) may be dened in the following manner: (n; m) = f(a; b) : uav = ubv; 8u 2 Sn; v 2 Smg; where Sk for k ..."
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A semigroup S is said to be structurally regular if there exists an ordered pair (n; m) of nonnegative integers such that the quotient S=(n; m) is regular in the usual sense. The congruence (n; m) may be dened in the following manner: (n; m) = f(a; b) : uav = ubv; 8u 2 Sn; v 2 Smg; where Sk for k
Certain Regular Semigroups of Infinite Matrices
"... Abstract: Let F be a field and N the set of natural numbers. It is known that the multiplicative semigroup of all bounded N × N matrices over F is a regular semigroup. Our purpose is to consider the multiplicative semigroup U∗(F) of all column bounded upper triangular N × N matrices A over F with fo ..."
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Abstract: Let F be a field and N the set of natural numbers. It is known that the multiplicative semigroup of all bounded N × N matrices over F is a regular semigroup. Our purpose is to consider the multiplicative semigroup U∗(F) of all column bounded upper triangular N × N matrices A over F
A HOMOMORPHISM THEOREM FOR SEMIGROUPS
"... If S = S ° is a semigroup which has a Orestricted completely 0simple homomorphic image then it is known that S need not have a maximal completely 0simple homomorphic image. The main theorem of this paper shows that although this is true for homomorphisms onto it is not the case when we consider ..."
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) the class of all regular semigroups; (c) the class of all regular bisimple semigroups. In general, and in these three cases in particular, (ii) does not hold. However, if # is one of the following classes, both (i) and (ii) are satisfied. (d) the class of all inverse semigroups; (e) the class of all
On Maximal Subgroups of Free Idempotent Generated Semigroups
, 2009
"... We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free ..."
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Cited by 12 (6 self)
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regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. 2000 Mathematics Subject Classification: 20M05, 20F05. 1 Introduction and summary of results Let S be a semigroup, and let E = E
Results 1  10
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