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)∈(E)CP(E),c(E)cN(E)cS(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.