This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinator...In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.展开更多
In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and cont...On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].展开更多
In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has...A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.展开更多
Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) o...A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.展开更多
In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some propert...In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.展开更多
In this paper, we discussed w-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In &...In this paper, we discussed w-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.展开更多
基金supported by the National Natural Science Foundation of China under grant No.11171222the Doctoral Program of the Ministry of Education under grant No.20094407120001
文摘This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
文摘In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.
基金The research of the second author was supported by the NSFC (10871161)
文摘In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
文摘On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].
文摘In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
基金supported by National Natural Science Foundation of China(11301077,11301078,11401097,11501108)Natural Science Foundation of Fujian Province(2015J01579,2016J05001)
文摘A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.
文摘Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
基金Supported by NSFC grant No. 10371002 (Y. Chang) and No.19901008 (J. Lei)
文摘A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.
文摘In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.
基金Supported by the NNSF of China(6047303060773035)
文摘In this paper, we discussed w-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.
