西北师范大学学报(自然科学版)
西北師範大學學報(自然科學版)
서북사범대학학보(자연과학판)
JOURNAL OF NORTHWEST NORMAL UNIVERSITY(NATURAL SCIENCE)
2015年
4期
14-17
,共4页
Dc-投射模%半对偶模%优越扩张%局部化
Dc-投射模%半對偶模%優越擴張%跼部化
Dc-투사모%반대우모%우월확장%국부화
Dc-projective modules%semidualizing modules%excellent extension%localization
在环 R的优越扩张和局部化上研究相对于半对偶R‐模C的Ding‐投射模(即 Dc‐投射模)及其维数。证明了在环R的优越扩张 S 上, M是 Dc‐投射 R‐模当且仅当 S R M 是 DS RC‐投射 S‐模;M的 Dc‐投射维数等于 S R M 的DS磗 RC‐投射维数。
在環 R的優越擴張和跼部化上研究相對于半對偶R‐模C的Ding‐投射模(即 Dc‐投射模)及其維數。證明瞭在環R的優越擴張 S 上, M是 Dc‐投射 R‐模噹且僅噹 S R M 是 DS RC‐投射 S‐模;M的 Dc‐投射維數等于 S R M 的DS磗 RC‐投射維數。
재배 R적우월확장화국부화상연구상대우반대우R‐모C적Ding‐투사모(즉 Dc‐투사모)급기유수。증명료재배R적우월확장 S 상, M시 Dc‐투사 R‐모당차부당 S R M 시 DS RC‐투사 S‐모;M적 Dc‐투사유수등우 S R M 적DS전 RC‐투사유수。
The Ding‐projective modules and its dimension with respect to a semidualizing R‐module C(that is ,Dc‐projective modules) are investigated under excellent extension and localization of a ring . It is proved that M is Dc‐projective R‐modules if and only if S R M is DS RC‐projective S‐modules , and that the Dc‐projective dimension of M is equal to the DS RC‐dimen‐sion of S R M .