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词汇 Singular submodule
分类 英语词汇 英语翻译词典
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Singular submodule

英语百科

Singular submodule

In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as \mathcal{Z}(M)=\{m\in M \mid \mathrm{ann}(m)\subseteq_e R\}\,. For general rings, \mathcal{Z}(M) is a good generalization of the torsion submodule tors(M) which is most often defined for domains. In the case that R is a commutative domain, tors(M)=\mathcal{Z}(M).

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