This paper defines the extensions of a lattice homomorphism on sublattice lattices andideal lattices,and gives strict proof to the properties they possess.
本文给出了格同态在子格格与理想格上的扩张的定义，并分别论证了他们所具有的性质。
AM-compact operator and o-weakly compact operator and lattice ho-momorphism are three kinds of important operators on Banach lattice,The thesis discuss the problems about the factorization of AM-compact operators,the condition for every o-weakly compact operator is AM-compact,the factorization of lattice homomorphism are also included.
AM-紧算子,ο-弱紧算子,格同态是Banach格上三类非常重要的算子,本文在阐述了相关历史背景和预备知识后,主要讨论研究了AM-紧算子的分解性,ο-弱紧算子与AM-紧算子的关系,以及格同态的分解性,主要为:第一部分较为简要的阐述了相关历史背景和预备知识,再现了无数数学前辈们在这方面的杰出工作,这也是本文的理论基础和依据。
The act of an ordered semigroup on a poset is extended into a lattice ordered semigroup on a lattice;the notion of S-lattices is introduced;and the properties of S-lattices congruence and S-lattices morphism are discussed to develop the representation theorems of lattice ordered semigroups.
将序半群在偏序集上的作用推广到格半群在格上的作用,提出了S-格的定义并讨论了S-格同态和S-格同余的性质,得到了格半群的表示定理。
In particular,a semi-Lattice homomorphism theorem is obtained.
特别地,得到了SPO(S)到PO(S)的半格同态定理。
In particular,two theorems on semi-lattice homomorphisms are obtained.
特别地,得到了SPO(S)到PO(S)的2个半格同态定理。
Prelattice and prelattice homomorphisms are introduced,and the relation of prelattice homomorphism and order homomorphism is studied.
引入了预格和预格同态的概念,研究了预格同态与序同态的关系,得到了预格同态是序同态的结论,并给出了预格同构的等价刻画,证明了预格间的映射是预格同构当且仅当它是序同构。