On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

具有逆断面的正规纯正半群

A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruces on a normal orthodox semigroup with an iverse transversal .A structure theorem for such semigroup is obtained.Munn(1966)gave a fundamental inverse semigroup Following Munn‘s idea ,we give a fundamental normal orthodox semigroup with an inverse transversal.     

A construction of weakly inverse semigroups

Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.     

三对角逆M-矩阵

In this paper we study a class of inverse M-matrices:tridiagonal inverse M-matrices,Graph theory is used to discuss the structure and properties of tridiagonal inverse M-matrices,A sufficient and necessary condtion for a nonnegative tridiagonal matrix to be an inverse M-matrix is given.Finally,it is proved that the set of the inverses of M-matrices with unipathic is closed under Hadamard product.     

On E-solid Regular Semigroups With Inverse Transversals

Let S be a regular semigroup. An inverse subsemigroup S of S is called an inverse transversal if So contains an unique inverse x" for each x E S. In this case, I ~ {e E E(S)lee = e}and A = {g 6 E(S)gg = g}, are left and right regular subbands of S, respectively, where E(S)denotes the set of idempotehts in S. Denote E' = E(S). A regular semigroup S is calledE-solid if R|E(S) o LIE(S) = LIE(S) o R|E(s). A regular semigroup S is E-solid if and only ifthere is an inverse congruence…     

0-Semidistributive Inverse Semigroups

For an inverse semigroup S,the set L(S)of all inverse subsemigroups(including the empty set)of S forms a lattice with respect to intersection denoted as usual by ∩ and union,where the union is the inverse subsemingroup generated by inverse subsemigroups A,B of S.The set     

纯正半群上的同余

Let S be an orthodox semigroup and γ the least inverse congruence on S. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ. the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence p on S can be uniquely determined by the admissible triple induced by p, and there exists a lattice isomomorphism between C(S) and Ca(S).     

Fixed Points and Asymptotic Behavior for Asymptotically Nonexpansive Type Semigroups in Banach Spaces

Let X be a Banach space with a weakly continuous duality map Jψ, C a non-empty weakly compact convex subset of X, and T = (T(t) : t ∈ S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K ∩ F(T) ≠ (?) is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].     

O-Semidistributive Inverse Semigroups

For an inverse semigroup S, the set L(S) of all inverse subsemigroups (including the emptyset) of S forms a lattice with respect to intersection denoted as usual by ∩ and union, wherethe union is the inverse subsemigroup generated by inverse subsemigroups A, B of S. The setLF(S) of all full inverse subsemigroups of S forms a complete sublattice of L(S), with E_s as     

右逆半群上的偏序关系

It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a fight inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.     

完全单半群及完全正则半群的逆断面

指出完全单半群Ｓ的任何一个Ｆ－类是逆断面,且为Ｑ－逆断面,而Ｓ的任何一个逆断面必是一个Ｆ－类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。     

具有E—逆断面的正则半群的结构定理

讨论了具有E－逆断面的正则半群的性质;并给出了具有E－逆断面的正则半群的一种结构定理。     

Naturally ordered regular semigroups with an inverse monoid transversal

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.     

On Inverse Transversals of Ordered Regular Semigroups

We first consider an ordered regular semigroup S in which every element has a biggest inverse and determine necessary and sufficient conditions for the subset S ^○ of biggest inverses to be an inverse transversal of S. Such an inverse transversal is necessarily weakly multiplicative. We then investigate principally ordered regular semigroups S with the property that S ^○ is an inverse transversal. In such a semigroup we determine precisely when the set S ^☆ of biggest pre-inverses is a subsemigroup and show that in this case S ^☆ is itself an inverse transversal of a subsemigroup of S. The ordered regular semigroup of 2 × 2 boolean matrices provides an informative illustrative example. The structure of S, when S ^☆ is a group, is also described.     

On the Continuity of Inversion in Countably Compact Inverse Topological Semigroups

Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x x^-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．