摘要
在效应代数中引入了正则元和正规元的概念并研究了它们的性质.首先证明了C(E)N(E)P(E),C(E)N(E)S(E),其中N(E)是效应代数E的所有正规元组成的集合,R(E)是所有正则元组成的集合.其次证明了R(E)和N(E)是E的正规子效应代数,且N(E)是正交模偏序集.此外还证明了若E是格序效应代数,则R(E)和N(E)都是E的子格,且N(E)是正交模格.
In the paper, the concepts of regular elements and normal elements in effect algebras are introduced, and some properties of them are studied. Firstly, it is shown that C（E）∈N （E）∈P（E） and C（E）∈N（E）∈S（E）, in which N（E） is the set of all normal elements in an effect algebra E and R（E） is the set of all regular elements in an effect algebra E. Secondly, it is proved that R（E）,N（E） are all normal sub-effect algebras of E, N（E） is an orthomodular poset. Moreover, if E is a lattice effect algebra, then it is proved that R（E） ,N（E） are all full sub-lattices of E and N（E） is an orthomodular lattice.
出处
《纺织高校基础科学学报》
CAS
2013年第2期143-148,共6页
Basic Sciences Journal of Textile Universities
基金
Supported by the National Natural Science Foundation of China(11271297)
the Foundation of Shaanxi Province(12JK853)
作者简介
Biogrophy： LI Hai-yang （1975- ）, male, a native of Fuping county, Shaanxi province, associate professor of Xi＇ an Polytechnic University. E-mail： Iplihaiyang@ 126. com
