Generalized affine transformation monoid of a residue class ring

作者：Cao Yonglin

来源：Semigroup Forum, 2007, 74(2): 259-273.

DOI：10.1007/s00233-005-0653-y

In this paper, we consider the generalized affine transformation monoid Gaff(All) of a residue class ring A/I of a commutative ring A with identity modulo its nonzero ideal I. For the general case, we investigate the Green's relations, Schutzenberger group for every D-class and, the structure of group R-classes, regular D-classes, the idempotent set E(Gaff (A/I)) and the regular element set Reg(Gaff (A/I)) of Gaff (A/I). If A is an integral domain and I a product of powers of invertible maximal ideals, we show that Gaff (A/I) is an epigroup, every R*-classes of Gaff (A/I) is a nil-extension of a right group and that Gaff (A/I) is a complete lattice of nil-extensions of right groups.

• 出版日期2007-4
• 单位山东理工大学