赵良.$(m,d)$-内射盖与Gorenstein $(m,d)$-平坦模[J].数学研究及应用,2016,36(5):527~536
$(m,d)$-内射盖与Gorenstein $(m,d)$-平坦模
$(m,d)$-Injective Covers and Gorenstein $(m, d)$-Flat Modules
投稿时间:2015-10-23  最后修改时间:2016-03-18
DOI:10.3770/j.issn:2095-2651.2016.05.004
中文关键词:  $(m,d)$-内射盖  Gorenstein $(m,d)$-平坦模  Gorenstein $(m,d)$-内射模  强Gorenstein $(m,d)$-平坦模
英文关键词:$(m, d)$-injective cover  Gorenstein $(m, d)$-flat module  Gorenstein $(m, d)$-injecitve module  strongly Gorenstein $(m, d)$-flat module
基金项目:安徽省高校省级自然科学基金 (Grant No.KJ2012Z028).
作者单位
赵良 安徽工业大学数理科学与工程学院, 安徽 马鞍山 243032 
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中文摘要:
      研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果.
英文摘要:
      We consider the conditions under which the class of $(m, d)$-injective $R$-modules is (pre)covering. It is shown that every left $R$-module over a left $(m, d)$-coherent ring has an $(m, d)$-injective cover. Moreover, the classes of Gorenstein $(m, d)$-flat modules and Gorenstein $(m, d)$-injecitve modules are introduced and studied. For a right $(m, d)$-coherent ring $R$, we prove that a left $R$-module $M$ is Gorenstein $(m, d)$-flat if and only if $M^{+}$ is Gorenstein $(m, d)$-injective as a right $R$-module. Some results on Gorenstein flat modules and Gorenstein $n$-flat modules are generalized.
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