Commutative Ring of the Idealization of aModule

• Main Authors: Ya-Jung Tsai, 蔡亞蓉
• Other Authors: Hsin-Ju Wang
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/89176078834401756400

碩士 === 國立中正大學 === 應用數學研究所 === 102 === Let R be a commutative ring with identity and I be an ideal of R. Let Z(R) be its set of zero-divisors and we use Z(R)\{0} to denote the set of nonzero zero-divisors of R. We nd all nite rings R such that (R(+)I) are bipar- tite or planar or toroidal. In this paper, we study a commutative ring extensions of R. When the idealization of I in R, denoted by (R(+)I) , introduced by Nagata [1]. In this note, we are able to nd the genera of (R(+)I).