bimodule

Let R and S be rings. An (R,S)-bimodule isan abelian group M which is a left module over R and a rightmodule over S such that the r(ms)=(rm)s holdsfor each r in R, m in M, and s in S.Equivalently, M is an (R,S)-bimodule if it is a leftmodule over $R\\otimes{S}^{\\,\\mathrm{op}}$ or a right module over ${R}^{\\,\\mathrm{op}}\\otimes S$ .

When M is an (R,S)-bimodule, we sometimes indicate thisby writing the module as ${}_{R}M_{S}$ .

If P is a subgroup of M which is also an(R,S)-bimodule, then P is an(R,S)-subbimodule of M.

单词	Bimodule
释义	bimodule Let R and S be rings. An (R,S)-bimodule isan abelian group M which is a left module over R and a rightmodule over S such that the r(ms)=(rm)s holdsfor each r in R, m in M, and s in S.Equivalently, M is an (R,S)-bimodule if it is a leftmodule over $R\\otimes{S}^{\\,\\mathrm{op}}$ or a right module over ${R}^{\\,\\mathrm{op}}\\otimes S$ . When M is an (R,S)-bimodule, we sometimes indicate thisby writing the module as ${}_{R}M_{S}$ . If P is a subgroup of M which is also an(R,S)-bimodule, then P is an(R,S)-subbimodule of M.
随便看	methods to find extremum MetricallyConvexSpace Metrically Convex Space MetricEntropy metric entropy MetricEquivalence metric equivalence MetricSpace metric space MetricSpacesAreHausdorff metric spaces are Hausdorff MetricSuperfields metric superfields MetricSystem metric system Metrizable metrizable MeusniersTheorem Meusnier’s theorem MHStonesRepresentationTheorem M. H. Stone’s representation theorem MianChowlaSequence Mian-Chowla sequence MichaelFrancisAtiyah Michael Francis Atiyah