In this paper, the half-strong endomorphisms of the join of split graphs are investigated. We give the conditions under which the half-strong endomorphisms of the join of split graphs form a monoid.
In this paper,the half-strong,the locally strong and the quasi-strong endomorphisms of a split graph are investigated.Let X be a split graph and let End(X),hEnd(X),lEnd(X) and qEnd(X) be the endomorphism monoid,the se...In this paper,the half-strong,the locally strong and the quasi-strong endomorphisms of a split graph are investigated.Let X be a split graph and let End(X),hEnd(X),lEnd(X) and qEnd(X) be the endomorphism monoid,the set of all half-strong endomorphisms,the set of all locally strong endomorphisms and the set of all quasi-strong endomorphisms of X,respectively.The conditions under which hEnd(X) forms a submonoid of End(X) are given.It is shown that lEnd(X) = qEnd(X) for any split graph X.The conditions under which lEnd(X)(resp.qEnd(X)) forms a submonoid of End(X) are also given.In particular,if hEnd(X) forms a monoid,then lEnd(X)(resp.qEnd(X)) forms a monoid too.展开更多
As well known, a normal orthogroup is a strong semilattice of rectangular groups. In this paper, we consider the homomorphisms between normal orthogroups and endomorphisms of themselves, relating them to the homomorph...As well known, a normal orthogroup is a strong semilattice of rectangular groups. In this paper, we consider the homomorphisms between normal orthogroups and endomorphisms of themselves, relating them to the homomorphisms and endomorphisms of the underlying rect-angular groups with their compositions.展开更多
In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition, the number of them is also given.
In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.
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
基金Supported by National Natural Science Foundation of China (Grant Nos. 10571077 and 10971053)
文摘In this paper, the half-strong endomorphisms of the join of split graphs are investigated. We give the conditions under which the half-strong endomorphisms of the join of split graphs form a monoid.
基金supported by National Natural Science Foundation of China(Grant Nos. 10571077,10971086)
文摘In this paper,the half-strong,the locally strong and the quasi-strong endomorphisms of a split graph are investigated.Let X be a split graph and let End(X),hEnd(X),lEnd(X) and qEnd(X) be the endomorphism monoid,the set of all half-strong endomorphisms,the set of all locally strong endomorphisms and the set of all quasi-strong endomorphisms of X,respectively.The conditions under which hEnd(X) forms a submonoid of End(X) are given.It is shown that lEnd(X) = qEnd(X) for any split graph X.The conditions under which lEnd(X)(resp.qEnd(X)) forms a submonoid of End(X) are also given.In particular,if hEnd(X) forms a monoid,then lEnd(X)(resp.qEnd(X)) forms a monoid too.
基金Supported by General Scientific Research Project of Shanghai Nor mal University (No.SK200707)Shanghai Shuguang Project (No.07SG38)
文摘As well known, a normal orthogroup is a strong semilattice of rectangular groups. In this paper, we consider the homomorphisms between normal orthogroups and endomorphisms of themselves, relating them to the homomorphisms and endomorphisms of the underlying rect-angular groups with their compositions.
文摘In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition, the number of them is also given.
基金Supported by the National Natural Science Foundation of China(10801117)
文摘In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.
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.
