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Rolando E. Peinado 《Semigroup Forum》1970,1(1):189-208
The set of elements of an (associative) ring under multiplication form a semigroup, but not every semigroup is isomorphic
to the multiplicative structure of a ring. The class of all multiplicative semigroups of all rings can not be described axiomatically.
Nevertheless for unique-addition rings, for finite rings and other special cases interesting characterizations can be given.
An abbreviated version was presented at the Symposium on Semigroups and the Multiplicative Structure of Rings held at the
University of Puerto Rico-Mayaguez, March 9–13, 1970. 相似文献
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Ryszard Mazurek 《Semigroup Forum》2011,83(2):335-342
A right-chain semigroup is a semigroup whose right ideals are totally ordered by set inclusion. The main result of this paper
says that if S is a right-chain semigroup admitting a ring structure, then either S is a null semigroup with two elements or sS=S for some s∈S. Using this we give an elementary proof of Oman’s characterization of semigroups admitting a ring structure whose subsemigroups
(containing zero) form a chain. We also apply this result, along with two other results proved in this paper, to show that
no nontrivial multiplicative bounded interval semigroup on the real line ℝ admits a ring structure, obtaining the main results
of Kemprasit et al. (ScienceAsia 36: 85–88, 2010). 相似文献
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M. Satyanarayana 《Semigroup Forum》1973,6(1):189-197
We shall consider semigroups with O, which contain a unique maximal right ideal generated by a finite number of independent
generators and in which every proper right ideal is contained in the unique maximal right ideal and investigate when these
semigroups are multiplicative semigroups of a ring. We prove in particular that the necessary condition for this class of
semigroups S to admit ring structure is S=S2 if |S|>2. Furthermore the admissible ring structure of S is determined when the product of every two generators of the maximal
right ideal M is O and when S satisfies one of the two conditions, namely S is commutative without idempotents except O and
1 or every generator of M is nilpotent. 相似文献
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M. Satyanarayana 《Semigroup Forum》1980,19(1):307-312
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The purpose of this paper is to investigate under what conditions an inverse semigroup M is isomorphic to the syntactic monoid M(A)* of afinite prefix code A over an alphabet X. We find a necessary condition for this to happen. It expresses a precise link between the group of units of M and the maximal subgroups of the 0-minimal ideal of M (Theorem 2.1). The condition is shown to be sufficient in case M is an ideal extension of a Brandt semigroup by a group (Corollary 2.3). We also introduce and study stable codes (products of subsets of the alphabet) and give structural properties of their syntactic monoids (Proposition 3.3 and Theorem 3.5). Most of our results inter-relate structural properties of certain semigroups and divisibility of integers attached to them. The terminology follows [1] and [3]. 相似文献
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Sándor Jenei 《Archive for Mathematical Logic》2003,42(5):489-514
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical
characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard
algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows
from their other axioms.
Received: 7 January 2002 / Revised version: 4 April 2002 /
Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics 相似文献
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Green's Lemma [1, Lemma 2.2] is one of the most important theorems in the theory of semigroups. The main purpose of this note is to establish a generalized Green's Lemma and a generalized Clifford and Miller's Theorem [1, p. 59] in linear semigroups. A generalized Green's Lemma describes the behavior of certain mappings between two distinct D-classes. 相似文献
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In Billhardt et al. (Semigroup Forum 79:101–118, 2009) the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in Blyth et al. (Glasgow Math. J. 36:163–171, 1994). The main result of the present paper, Theorem 2.15, establishes that a regular semigroup S with an associate inverse subsemigroup S ? satisfies three simple identities if and only if it is isomorphic to a generalised Rees matrix semigroup M(T;A,B;P), where T is a Clifford semigroup, A and B are bands, with common associate inverse subsemigroup E(T) satisfying the referred identities, and P is a sandwich matrix satisfying some natural conditions. If T is a group and A, B are left and right zero semigroups, respectively, then the structure described provides a usual Rees matrix semigroup with normalised sandwich matrix, thus generalising the Rees matrix representation for completely simple semigroups. 相似文献
14.
On the structure of semigroups of idempotent matrices 总被引:1,自引:0,他引:1
Karin Cvetko-Vah 《Linear algebra and its applications》2007,426(1):204-213
We prove that any pure regular band of matrices admits a simultaneous LU decomposition in the standard form. In case that such a band forms a double band called a skew lattice, we obtain the standard form without the assumption of purity. 相似文献
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This paper gives some equivalent definitions of stronglyP-regular semigroups and characterizes the structure ofP-regular semigroups as the spined product of fundamentalP-regular semigroups and regular *-semigroups.
This work is supported by the National Nature Science Foundation of China. 相似文献
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We prove that any Lie algebra g over a field K of characteristic zero admitting a unique up to a constant quadratic structure is necessarily a simple Lie algebra. If the field K is algebraically closed, such condition is also sufficient. Further, a real Lie algebra g admits a unique quadratic structure if and only if its complexification gC is a simple Lie algebra over C 相似文献
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