首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 78 毫秒
1.
Let S be an eventually regular semigroup. The extensively P-partial congruence pairs and P-partial congruence pairs for S are defined. Furthermore, the relationships between the lattice of congruences on S, the lattice of P-partial kernel normal systems for S, the lattice of extensively P-partial kernel normal systems for S and the poset of P-partial congruence pairs for S are explored.  相似文献   

2.
Regular congruences on an E-inversive semigroup   总被引:1,自引:0,他引:1  
  相似文献   

3.
As a generalization of Preston’s kernel normal systems, P\mathcal{P}-kernel normal systems for P\mathcal{P}-inversive semigroups are introduced, and strongly regular P\mathcal{P}-congruences on P\mathcal{P}-inversive semigroups in terms of their P\mathcal{P}-kernel normal systems are characterized. These results generalize the corresponding results for P\mathcal{P}-regular semigroups and P\mathcal{P}-inversive semigroups.  相似文献   

4.
An ordered regular semigroup S is E-special if for every x ∈ S there is a biggest x + ∈ S such that both xx + and x + x are idempotent. Every regular strong Dubreil–Jacotin semigroup is E-special, as is every ordered completely simple semigroup with biggest inverses. In an E-special ordered regular semigroup S in which the unary operation x → x + is antitone the subset P of perfect elements is a regular ideal, the biggest inverses in which form an inverse transversal of P if and only if S has a biggest idempotent. If S + is a subsemigroup and S does not have a biggest idempotent, then P contains a copy of the crown bootlace semigroup.  相似文献   

5.
M. Sedaghatjoo  V. Laan 《代数通讯》2013,41(11):4019-4030
For a monoid S, the set S × S equipped with the componentwise right S-action is called the diagonal act of S and is denoted by D(S). A monoid S is a left PP (left PSF) monoid if every principal left ideal of S is projective (strongly flat). We shall call a monoid S left P(P) if all principal left ideals of S satisfy condition (P). We shall call a monoid S weakly left P(P) monoid if the equalities as = bs, xb = yb in S imply the existence of r ∈ S such that xar = yar, rs = s. In this article, we prove that a monoid S is left PSF if and only if S is (weakly) left P(P) and D(S) is principally weakly flat. We provide examples showing that the implications left PSF ? left P(P) ? weakly left P(P) are strict. Finally, we investigate regularity of diagonal acts D(S), and we prove that for a right PP monoid S the diagonal act D(S) is regular if and only if every finite product of regular acts is regular. Furthermore, we prove that for a full transformation monoid S = 𝒯 X , D(S) is regular.  相似文献   

6.
This paper deals with anR danalogue of a theorem of Valentine which states that a closed 3-convex setS in the plane is decomposable into 3 or fewer closed convex sets. In Valentine’s proof, the points of local nonconvexity ofS are treated as vertices of a polygonP contained in the kernel ofS, yielding a decomposition ofS into 2 or 3 convex sets, depending on whetherP has an even or odd number of edges. Thus the decomposition actually depends onc(P′), the chromatic number of the polytopeP′ dual toP. A natural analogue of this result is the following theorem: LetS be a closed subset ofR d, and letQ denote the set of points of local nonconvexity ofS. We require thatQ be contained in the kernel ofS and thatQ coincide with the set of points in the union of all the (d − 2)-dimensional faces of somed-dimensional polytopeP. ThenS is decomposable intoc(P′) closed convex sets.  相似文献   

7.
A regular {v, n}-arc of a projective space P of order q is a set S of v points such that each line of P has exactly 0,1 or n points in common with S and such that there exists a line of P intersecting S in exactly n points. Our main results are as follows: (1) If P is a projective plane of order q and if S is a regular {v, n}-arc with n ≥ √q + 1, then S is a set of n collinear points, a Baer subplane, a unital, or a maximal arc. (2) If P is a projective space of order q and if S is a regular {v, n}-arc with n ≥ √q + 1 spanning a subspace U of dimension at least 3, then S is a Baer subspace of U, an affine space of order q in U, or S equals the point set Of U. © 1993 John Wiley & Sons, Inc.  相似文献   

8.
Summary Let a regular Borel measure m on a locally compact semigroup S be upper semi-invariant i.e., m(C x)m(C) and m(x C)m(C) for every compact C and x in S. It is shown: (i) Every subsemigroup of S of positive measure contains an idempotent. (ii) S admits an upper semi-invariant probability measure iff S has a kernel K which is a compact group.We should like to thank the referee for pointing out certain redundancies in the theorems. Also we thank Dr. Tze-Chien Sun for some helpful observations.  相似文献   

9.
In this paper, purity of S-posets over a pomonoid S is investigated. We first study some basic properties of absolutely po-pure S-posets. Among other results, it is proved that every regular injective S-poset is absolutely po-pure, and every absolutely po-pure inequationally compact S-poset is regular injective. Then, using the notion of semi-finitely presented S-poset based on the finitely induced S-poset congruence, we find an equivalent condition for an S-poset to be 1-po-pure in a regular extension. Finally, a characterization of an absolutely 1-po-pure S-poset is presented.  相似文献   

10.
In some recent works we have developed a new functional calculus for bounded and unbounded quaternionic operators acting on a quaternionic Banach space. That functional calculus is based on the theory of slice regular functions and on a Cauchy formula which holds for particular domains where the admissible functions have power series expansions. In this paper, we use a new version of the Cauchy formula with slice regular kernel to extend the validity of the quaternionic functional calculus to functions defined on more general domains. Moreover, we show some of the algebraic properties of the quaternionic functional calculus such as the S-spectral radius theorem and the S-spectral mapping theorem. Our functional calculus is also a natural tool to define the semigroup e tA when A is a linear quaternionic operator.   相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号