Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If ...Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. （2） If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤eM if and only if there exists I ≤ R such that N = （0 ：M I）. （3） If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.展开更多
Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of ...Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of second submodules of M and the spectrum Spec-c（M） of coprime submodules of M, study several properties of these spaces and investigate their internlay with the algebraic properties of M.展开更多
文摘Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. （2） If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤eM if and only if there exists I ≤ R such that N = （0 ：M I）. （3） If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.
文摘Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of second submodules of M and the spectrum Spec-c（M） of coprime submodules of M, study several properties of these spaces and investigate their internlay with the algebraic properties of M.
