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FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS
, 2007
"... The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider a ..."
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The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider
Onesided bases of semigroups
 Mat. Õas
, 1972
"... The structure of semigroups, containing onesided bases is investigated in [1]. The notion of a onesided base was introduced by T a m u r a in [4]. The purpose of the present paper is to describe the structure of semigroups containing twosided bases. A sLibset A of a semigroup S is a right (left) ..."
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S, thus (a)T C (b)T. Lemma 2. Let A be a twosided base of a semigroup S. If a,b e A, a =J = b, then neither a <b, nor b < a. Proof. Let us assume that a <b, (a)T C (b)T. If there were a 4 = b, then a G (Sb U bS U SbS). Lemma 1 implies that a = b. Theorem 1. A nonempty subset A of a semigroup
ABSOLUTELY FLAT SEMIGROUPS
"... All left modules over a ring are flat if and only if the ring is von Neumann regular. In [7], M. Kilp showed that for a monoid S to be left absolutely flat (i.e., for all left Ssets to be flat) regularity is necessary but not sufficient. Kilp also proved [8] that every inverse union of groups is ab ..."
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is absolutely flat. In the present paper we show that in fact every inverse semigroup is absolutely flat and that the converse is not true. 1. Preliminaries. We consider a monoid to be a universal algebra (S; , 1) of type (2,0). We shall consistently denote such a monoid by S and on occasion consider it to be a
SOME DECOMPOSITIONS OF SEMIGROUPS
"... Abstract. In this paper we will introduce the notion of aconnected elements of a semigroup, aconnected semigroups, and weakly externally commutative semigroup, and we prove that a weakly externally commutative semigroup is a semilattice of aconnected semigroups. Undefined notions can be found in ..."
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of semigroups of binary relations have been studied by Blyth and Hickey [1], Hickey [2,3]. A semigroup S is called Archimedean if, for every couple a, b ∈ S, there exists n ∈ Z+ such that an ∈ SbS. Let S be a commutative semigroup, a ∈ S, then (S, a) is also a commutative semigroup. By above mentioned (S, a
EMBEDDING OF COUNTABLE TOPOLOGICAL SEMIGROUPS IN SIMPLE COUNTABLE CONNECTED TOPOLOGICAL SEMIGROUPS
"... We prove that any countable Hausdorff topological (inverse) semigroup is topologically isomorphically embedded into a simple countable connected Hausdorff topological (inverse) semigroup with identity. This work is a sequel to the author’s investigations in [1] and [2]. The terminology and notation ..."
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bU { , } and is defined by the relations ab = 1, as a = , and sb b = for all s S ∈ and also by the relations valid in S. The identity 1 of the semigroup C ()S is either the identity of the semigroup S if 1∈S or the identity added to C ()S in the usual way if S does not contain the identity
SEMIGROUPS OF COMPRESSED TOEPLITZ OPERATORS AND NEVANLINNA PICK INTERPOLATION
, 2004
"... The purpose of this paper is to determine conditions for an operator PBTA commuting with the compression SB of the standard unilateral shift on the Hardy space to a shift coinvariant subspace to embed in a C0semigroup of operators commuting with SB. For B an interpolating Blaschke product, a nece ..."
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The purpose of this paper is to determine conditions for an operator PBTA commuting with the compression SB of the standard unilateral shift on the Hardy space to a shift coinvariant subspace to embed in a C0semigroup of operators commuting with SB. For B an interpolating Blaschke product, a
A semigroup proof of the bounded degree case of S.B. Rao’s conjecture on degree sequences and a bipartite analogue
 J. Combin. Theory Ser. B
"... In this paper, we prove and use a fairly simple semigroup lemma to give a short proof of the bounded degree case of Rao's Conjecture that is independent of the ChudnovskySeymour structure theory. In fact, we affirmatively answer two questions of N. Robertson[7], the first of which implies the ..."
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In this paper, we prove and use a fairly simple semigroup lemma to give a short proof of the bounded degree case of Rao's Conjecture that is independent of the ChudnovskySeymour structure theory. In fact, we affirmatively answer two questions of N. Robertson[7], the first of which implies
Principal Ideal Graphs of Rees Matrix Semigroups
"... Let S be a finite regular semigroup. We define the principal left ideal graph of S as the graph SG with V (SG) = S and two vertices a and b (a = b) are adjacent in SG if and only if Sa ∩ Sb = {}. The principal right ideal graph is defined accordingly and is denoted by GS. The principal ideal grap ..."
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Let S be a finite regular semigroup. We define the principal left ideal graph of S as the graph SG with V (SG) = S and two vertices a and b (a = b) are adjacent in SG if and only if Sa ∩ Sb = {}. The principal right ideal graph is defined accordingly and is denoted by GS. The principal ideal
c © TÜB_ITAK ON CERTAIN VARIETIES OF SEMIGROUPS
"... In this paper we generalize the class of completely regular semigroups (unions of groups) to the class of local monoids, that is the class of all semigroups where the local subsemigroups aSa are local submonoids. The sublattice of this variety (L(L(M)) covers another lattice isomorphic to the lattic ..."
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to the lattice of all bands ([x2 = x]): Every bundvariety U has as image the variety − U; which is the class of all semigroups, where is a Ucongruence (ab, aSa = bSb): It is shown how one can nd the laws for −U for a given bandvariety U. The laws for −B are given and it is shown that −RB −L(G)L(V): = fS: a
EFFICIENT COMPUTATION IN GROUPS AND SIMPLICIAL COMPLEXES BY
"... Abstract. Using HNN extensions of the BooneBritton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time. Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators requi ..."
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to prove unsolvability results. The first, and most instructive, example was Post's simulation of Turing machines by finitely presented semigroups [10]. For each deterministic Turing machine M, Post constructs a semigroup T(M) on generators we shall call qa, sb, where a and A range over certain finite
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