共查询到20条相似文献,搜索用时 125 毫秒
1.
It is known that a simple Bézout domain is the domain of elementary divisors if and only if it is 2-simple. The block-diagonal
reduction of matrices over an n -simple Bézout domain (n ≥ 3) is realized. 相似文献
2.
《数学学报(英文版)》2015,(7)
A semigroup is called completely J~((e))-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid.It is proved that completely J~((e))-simple semigroups form a quasivarr ity.Moreover,the construction of free completely J~((e))-simple semigroups is given.It is found that a free completely J~((e))-simple semigroup is just a free completely J~*-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
3.
We prove that, in a domain of elementary divisors, the intersection of all nontrivial two-sided ideals is equal to zero. We
also show that a Bézout domain with finitely many two-sided ideals is a domain of elementary divisors if and only if it is
a 2-simple Bézout domain. 相似文献
4.
5.
In τ-tilting theory, it is often difficult to determine when a set of bricks forms a 2-simple minded collection. The aim of this paper is to determine when a set of bricks is contained in a 2-simple minded collection for a τ-tilting finite algebra. We begin by extending the definition of mutation from 2-simple minded collections to more general sets of bricks (which we call semibrick pairs). This gives us an algorithm to check if a semibrick pair is contained in a 2-simple minded collection. We then use this algorithm to show that the 2-simple minded collections of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) are given by pairwise compatibility conditions if and only if every vertex in the corresponding quiver has degree at most 2. As an application, we show that the classifying space of the τ-cluster morphism category of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) is an Eilenberg-MacLane space if every vertex in the corresponding quiver has degree at most 2. 相似文献
6.
A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups. 相似文献
7.
R.R. Zapatrin 《Semigroup Forum》1999,59(1):121-125
L the explicit construction of a 0-simple Rees matrix semigroup is suggested such that the lattice of left annihilators of this semigroup is isomorphic to L. 相似文献
8.
Roman S. Gigoń 《Semigroup Forum》2013,86(1):108-113
A semigroup S is called η-simple if S has no semilattice congruences except S×S. Tamura in (Semigroup Forum 24:77–82, 1982) studied η-simple semigroups with a unique idempotent. In the present paper we consider a more general situation, that is, we investigate η-simple semigroups (without zero) with a least idempotent. Moreover, we study η ?-simple semigroups with zero which contain a least non-zero idempotent. 相似文献
9.
In this paper, we consider the lattice Subf S of full subsemigroups of an inverse semigroup S. Our first main theorem states
that for any inverse semigroup S, Subf S is a subdirect product of the lattices of full subsemigroups of its principal factors,
so that Subf S is distributive [meet semidistributive, join semidistributive, modular, semimodular] if and only if the lattice
of full subsemigroups of each principal factor is. To examine such inverse semigroups, therefore, we need essentially only
consider those which are 0-simple. For a 0-simple inverse semigroup S (not a group with zero), we show that in fact each of
modularity, meet semidistributivity and join semidistributivity of Subf S is equivalent to distributivity of S, that is, S
is the combinatorial Brandt semigroup
with exactly two nonzero idempotents and two nonidempotents. About semimodularity, however, we concentrate only on the completely
0-simple case, that is, Brandt semigroups. For a Brandt semigroup S (not a group with zero), semimodularity of Subf S is equivalent
to distributivity of Subf S. Finally, we characterize an inverse semigroup S for which Subf S is a chain. 相似文献
10.
将Green关系推广到Green~-关系。给出了密码^ ~ H-富足半群的半格分解,利用此分解,证明了^ ~ H-富足半群为正规密码^H-富足半群当且仅当它是完全^ ~ H-单半群的强半格. 相似文献
11.
In this paper we analyze the so-called word problem for (finite)
combinatorial 0-simple semigroups and matrix semigroups from the viewpoint
of computational complexity. 相似文献
12.
13.
Jingjing Ma 《Algebra Universalis》2011,65(4):341-351
It is shown that a unital finite-dimensional ℓ-simple ℓ-algebra with a distributive basis is isomorphic to a lattice-ordered matrix algebra with the entrywise lattice order over
a lattice-ordered twisted group algebra of a finite group with the coordinatewise lattice order. It is also shown that the
isomorphism is unique. 相似文献
14.
本文证明了:(1)Exchange环R的K0群的正向凸子群格同构于R的稳定余有限半本原理想格;(2)稳定有限、半本原的exchange环R是单的当且仅当它是K0-单的并且满足逼近弱s^*—可比性,推广了Goodearl,Ara等人的结果。 相似文献
15.
《代数通讯》2013,41(6):2461-2479
Superabundant semigroups are generalizations of completely regular semigroups written the class of abundant semigroups. It has been shown by Fountain that an abundant semigroup is superabundant if and only if it is a semilattice of completely J *-simple semigroups. Reilly and Petrich called a semigroup S cryptic if the Green's relation H is a congruence on S. In this paper, we call a superabundant semigroup S a regular crypto semigroup if H * is a congruence on S such that S/H * is a regular band. It will be proved that a superabundant semigroup S is a regular crypto semigroup if and only if S is a refined semilattice of completely J *-simple semigroups. Thus, regular crypto semigroups are generalization of the cryptic semigroups as well as abundant semigroups. 相似文献
16.
Takeyoshi Kogiso Go Miyabe Miyuki Kobayashi Tatsuo Kimura. 《Mathematics of Computation》2003,72(242):865-889
In this paper, we shall construct explicitly irreducible relative invariants of two 2-simple prehomogeneous vector spaces. Together with a preprint by the same authors, this completes the list of all relative invariants of regular 2-simple prehomogeneous vector spaces of type I.
17.
证明了ο-超富足半群S是正规密码ο-超富足半群当且仅当它是完全Jο-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广。 相似文献
18.
M. Satyanarayana 《Semigroup Forum》1971,3(1):43-50
A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely
generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is
unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal
by single elements and semigroups which are generated by two independent generators and describes their structure. We also
prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero.
Communicated by A. H. Clifford 相似文献
19.
介绍完全零单半群上的真模糊同余和连接模糊三元组的概念,由此得到完全零单半群上的真模糊同余集和连接模糊三元组集之间的双射。 相似文献
20.
Let A2 be the variety generated by the five-element non-orthodox 0-simple
semigroup. This paper presents the identity bases for several subvarieties of
A2 that are not generated by any completely 0-simple or completely simple
semigroups. It will be shown that several subvarieties of A2, including the
variety generated by the five-element Brandt semigroup, are hereditarily finitely
based. 相似文献