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1.
Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline 总被引:2,自引:0,他引:2
Song Chol HAN Hong Xing LI 《数学学报(英文版)》2005,21(5):1093-1098
Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn(L) = PLn (L) for any n (n 〉 2), in which GLn(L) is the group of all n × n invertible matrices over L and PLn(L) is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice. 相似文献
2.
Li Lide 《数学年刊B辑(英文版)》1982,3(6):745-752
In this paper it is shown that the intersection of all w-relations of a hemiring R is exactly the intersection of all primitive relations of this hemiring, and is called J-relational radical of the himiring R. Several properties of the J-relational radical are described. The radical R of a hemiring R is defined by the set {x\in R|x\tau 0}, where \tau is the J-relational radical of R. We obtain independently following results: 1.R is a right quasi-regular ideal which contains every right quasi-regular right ideal. 2.R=\cap {(0:M)|M,, irreducible cancellative right R-semimodule. The term "Jacobson semisimple” in ring theory is generalized to hemirings by defining “J-relational semisimple.” It is proved that if \tau is the Jacobson relational radical of a hemiring R, then R/\tau is J-relational semisimple. Finally the structure theorem of the hemirings is given. A hemiring is J-relational simisimple if and only if it is isomorphic to a subdirect sum of completely primitive hemirings. 相似文献
3.
Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N). 相似文献
4.
Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR(ω) ∞ implies G-dimω(M) ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω(M) is finite. 相似文献
5.
In this paper, let m, n be two fixed positive integers and M be a right R-module, we define (m, n)-M-flat modules and (m, n)-coherent modules. A right R-module F is called (m, n)-M-flat if every homomorphism from an (n, m)-presented right R-module into F factors through a module in addM. A left S-module M is called an (m, n)-coherent module if MR is finitely presented, and for any (n, m)-presented right R-module K, Hom(K, M) is a finitely generated left S-module, where S = End(MR). We mainly characterize (m, n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules. Some properties of (m, n)-coherent rings and coherent rings are obtained as corollaries. 相似文献
6.
Let R be a ring. We consider left (or right) principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left (or right) principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent. 相似文献
7.
We provide estimates on the degree of C l GV determinacy ( G is one of Mather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C l G triviality of function germs given by M.A.S.Ruas. 相似文献
8.
The Semigroup Structure of Left
Clifford Semirings 总被引:5,自引:0,他引:5
YuQiGUO KarPingSHUM 《数学学报(英文版)》2003,19(4):783-792
In this paper,we generalize Clifford semirings to left Clifford semirings by means of the so-called band semirings.We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings. 相似文献
9.
We provide estimates on the degree of C l GV determinacy ( G is one of Mather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C l G triviality of function germs given by M.A.S.Ruas. 相似文献
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12.
Orthodox semigroups whose idempotents satisfy a certain identity 总被引:2,自引:0,他引:2
Miyuki Yamada 《Semigroup Forum》1973,6(1):113-128
An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy
[xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure
of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents
satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies
xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup. 相似文献
13.
F. Pastijn 《Semigroup Forum》1983,26(1):151-166
In [2] it is shown that every idempotent distributive semiring is the P?onka sum of a semilattice ordered system of idempotent distributive semirings which satisfy the generalized absorption law x+xyx+x=x. We shall show that an idempotent distributive semiring which satisfies the above absorption law must be a subdirect product of a distributive lattice and a semiring which satisfies the additional identity xyx+x+xyx=xyx. Using this, we construct the lattice of all equational classes of idempotent distributive semirings for which the two reducts are normal bands. 相似文献
14.
J. E. van den Berg 《Acta Mathematica Hungarica》2000,87(1-2):153-172
This paper investigates closure properties possessed by certain classes of finite subdirect products of prime rings. If ℳ
is a special class of prime rings then the class ℳ∞ of all finite subdirect products of rings in ℳ is shown to be weakly special. A ring S is said to be a right tight extension [resp. tight extension] of a subring R if every nonzero right ideal [resp. right ideal and left ideal] of S meets R nontrivially. Every hereditary class of semiprime rings closed under tight extensions is weakly special. Each of the following
conditions imposed on a semiprime ring yields a hereditary class closed under right tight extensions: ACC on right annihilators;
finite right Goldie dimension; right Goldie. The class of all finite subdirect products of uniformly strongly prime rings
is shown to be closed under tight extensions, answering a published question.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
The article discusses the structure of cyclic semirings with noncommutative addition. In the infinite case, the addition is idempotent and is either left or right. Addition of a finite cyclic semirings can be either idempotent or nonidempotent. In the finite additively idempotent cyclic semiring, addition is reduced to the addition of a cyclic subsemiring with commutative addition and an absorbing element for multiplication and the addition of a cycle that is a finite semifield. 相似文献
16.
A Characterization of Semirings Which Are Subdirect Products of a Distributive Lattice and a Ring 总被引:9,自引:0,他引:9
S. Ghosh 《Semigroup Forum》1999,59(1):106-120
E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi [2] in the case of Boolean semirings. 相似文献
17.
18.
Hanns Joachim Weinert 《Semigroup Forum》1984,28(1):313-333
In this paper we consider O-simple semirings S, where O denotes the multiplicative zero of S, which may be in particular the
additive neutral o of S at the same time. In this context we give some statements on matrix semirings and introduce contracted
semigroup semirings in §3, a matter of interest of its own. We further use our results to compare the usual concept of division
semirings with a new one introduced in [18], and we show that a corresponding theorem in [18] is in general only valid for
division semirings in the usual meaning.
Dedicated to E.S. Lyapin on his 70th birthday 相似文献
19.
In a series of papers, Green’s relations on the additive and multiplicative reducts of a semiring proved to be a very useful
tool in the study of semirings. However, in the vast majority of cases, Green’s relations are not congruences, and we show
that in such cases it is much more convenient to use the congruence openings of Green’s relations, instead of the Green’s
relations themselves. By means of these congruence openings we define and study several very interesting operators on the
lattices of varieties of semirings and additively idempotent semirings, and, in particular, we establish order embeddings
of the lattice of varieties of additively idempotent semirings into the direct products of the lattices of open (resp. closed)
varieties with respect to two opening (resp. closure) operators on this lattice that we introduced. 相似文献
20.
Note on a certain class of orthodox semigroups 总被引:1,自引:0,他引:1
Miyuki Yamada 《Semigroup Forum》1973,6(1):180-188
This is a continuation and also a supplement of the previous papers [5], [6] and [8] concerning orthodox semigroups1). In [8], it has been shown that a quasi-inverse semigroup is isomorphic to a subdirect product of a left inverse semigroup
and a right inverse semigroup. In this paper, we present a structure theorem for quasi-inverse semigroups and some relevant
matters. 相似文献