Multiplicative Semigroup of a Residue Class Ring |
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Authors: | Yonglin Cao |
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Institution: | (1) Schoolof Mathematics and Information, Shandong University of Technology, Zibo, Shandong 255049, China |
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Abstract: | In this paper, we consider the structure of the
multiplicative semigroup of a residue class ring R/I of a
commutative ring R with identity modulo its nonzero ideal I.
For the general case, we investigate the H-classes,
maximal subgroups and the structure of Reg(R/I) which
is the set of regular elements of R/I. If R is any integral
domain and if I is a product of powers of invertible maximal
ideals, we show that R/I is an epigroup, every
H*-class of R/I is a nil-extension of a group
(:unipotent epigroup) and that R/I is a complete lattice of
unipotent epigroups. |
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Keywords: | |
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