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MAXIMAL ORDERS IN COMPLETELY 0SIMPLE SEMIGROUPS
"... Fountain, Gould and Smith introduced the concept of equivalence of orders in a semigroup and the notion of a maximal order. We examine these ideas in the context of orders in completely 0simple semigroups with particular emphasis on abundant orders. ..."
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Fountain, Gould and Smith introduced the concept of equivalence of orders in a semigroup and the notion of a maximal order. We examine these ideas in the context of orders in completely 0simple semigroups with particular emphasis on abundant orders.
0TIGHT COMPLETELY 0SIMPLE SEMIGROUPS
, 2006
"... A semigroup is 0tight if each of its congruences is uniquely determined by each of the congruence classes which do not contain zero. We classify finite 0tight rectangular 0bands, and characterize 0tight completely 0simple semigroups. Finally, we obtain correspoding results about tight completel ..."
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A semigroup is 0tight if each of its congruences is uniquely determined by each of the congruence classes which do not contain zero. We classify finite 0tight rectangular 0bands, and characterize 0tight completely 0simple semigroups. Finally, we obtain correspoding results about tight
GENERATING SETS OF COMPLETELY 0SIMPLE SEMIGROUPS
"... A formula for the rank of an arbitrary finite completely 0simple semigroup, represented as a Rees matrix semigroup M 0 [G; I, Λ; P], is given. The result generalises that of Ruˇskuc concerning the rank of connected finite completely 0simple semigroups. The rank is expressed in terms of I, Λ, t ..."
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Cited by 5 (4 self)
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A formula for the rank of an arbitrary finite completely 0simple semigroup, represented as a Rees matrix semigroup M 0 [G; I, Λ; P], is given. The result generalises that of Ruˇskuc concerning the rank of connected finite completely 0simple semigroups. The rank is expressed in terms of I, Λ
On semigroups which are unions of completely 0simple semigroups
 Author's address: University of Wisconsin
, 1966
"... The WedderburnArtin and the Noether Structure Theorems give satisfactory characterizations of semisimple associative rings. In the paper KERTESZSTEINFELD [4] there are given some other characterizations of these rings. Rees ' well known Theorem for completely 0simple semigroups plays the sam ..."
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Cited by 1 (0 self)
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The WedderburnArtin and the Noether Structure Theorems give satisfactory characterizations of semisimple associative rings. In the paper KERTESZSTEINFELD [4] there are given some other characterizations of these rings. Rees ' well known Theorem for completely 0simple semigroups plays
Decidable and undecidable problems related to completely 0simple semigroups
, 1996
"... The undecidable problems of the title are concerned with the question: is a given finite semigroup embeddable in a given type of completely 0simple semigroups? It is shown, for example, that the embeddability of a (finite) 3nilpotent semigroup in a finite completely 0simple semigroup is decidabl ..."
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The undecidable problems of the title are concerned with the question: is a given finite semigroup embeddable in a given type of completely 0simple semigroups? It is shown, for example, that the embeddability of a (finite) 3nilpotent semigroup in a finite completely 0simple semigroup
Algorithmic Problems for Finite Groups and Finite 0Simple Semigroups
, 1996
"... It is shown that the embeddability of a finite 4nilpotent semigroup into a 0simple finite semigroup with maximal groups from a pseudovariety V is decidable if and only if the universal theory of the class V is decidable. We show that it is impossible to replace 4 by 3 in this statement. We also sho ..."
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It is shown that the embeddability of a finite 4nilpotent semigroup into a 0simple finite semigroup with maximal groups from a pseudovariety V is decidable if and only if the universal theory of the class V is decidable. We show that it is impossible to replace 4 by 3 in this statement. We also
CONGRUENCEFREE SIMPLE SEMIGROUP
"... Abstract. If a semigroup S has no nontrivial congruences then S is either simple or 0simple.([2]) By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0simple) semigroup may have a nontrivial congruence. Thus it is a short note for the ..."
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Abstract. If a semigroup S has no nontrivial congruences then S is either simple or 0simple.([2]) By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0simple) semigroup may have a nontrivial congruence. Thus it is a short note
On the irreducible representations of a finite semigroup
, 2007
"... Work of Clifford, Munn and Ponizovskiĭ parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and b ..."
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Cited by 27 (15 self)
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and by Lallement and Petrich. All of these approaches make use of Rees’s theorem characterizing 0simple semigroups up to isomorphism. Here we provide a short modern proof of the CliffordMunnPonizovskiĭ result based on a lemma of J. A. Green, which allows us to circumvent the theory of 0simple semigroups. A
MAXIMAL ORDERS IN SEMIGROUPS1
"... Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of ..."
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Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept
SEMIGROUPS WITH ASCENDING CHAIN CONDITION
"... A semigroup S is said to satisfy the ascending chain condition (a.c.c.) on right ideals if every chain of right ideals under setinclusion terminates at a finite stage. The class of semigroups with a.c.c. on right ideals includes the class of finite semigroups. In this paper we discuss some of the p ..."
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of the properties enjoyed by semigroups with a.c.c. and in particular those properties which the semigroups with a.c.c. share with semigroups which are finite. It is well known that a 0simple semigroup has no zerodivisors if and only if it has no proper nilpotent elements [1; 71]. Naturally one may ask what type
Results 1  10
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102