摘要
本文是在[1]的基础上,将半群S的幂等元集E(S)由理想推广为n-伪理想,然后来给出S的结构。本文未用到格林关系,因而证明有別于[1],而且[1]是我们的特例。
In this paper we define a kind of quasi-regular semigroup S. Tt has eight equivalent sayings: (i) E(S)≠ φ,S is a strong n—Pseudo Archimedes, (ii) Sis a torsion and (iii) S is a torsion, E(S) is a n-pseudo simple subsemigroup of S and is a double n-pseudo ideal of S; (iv) S is a torsion and then (v) S is a torsion, E(S) is a rectangular band and E(S) is a double n-pseudo idealof S; (vi) S is a torsion, E(S) is a rectangular band and E(S) is a n—Pseudo ideal of S; (vii) (viii) than and obtained the structure of S:is a partial semigroup is a rectangular band, such that if p(i,j)∈I× J, then p(ij) = (iξ_p,j) if(i,j)q∈I× J, then (i,j)q = (i,jη_4) these partial mappijngs satisfying:i) if and are all defined, then ii) if and are all defined, then and are all transformation of contant quantity. is a semigroup.
出处
《南京大学学报（自然科学版）》
CAS
CSCD
1992年第3期352-361,共10页
Journal of Nanjing University（Natural Science）
关键词
半群
正则元
矩形带
n-伪理想
Semigroup
regular element
rectangular band
n-pseudo ideal
