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In the various module generalizations of the concepts of prime (semiprime) for a ring, the question ``when are semiprime modules subdirect product of primes?" is a serious question in this context and it is considered by earlier authors in the literature. We continue study on the above question by showing that: If $R$ is Morita equivalent to a right pre-duo ring (e.g., if $R$ is commutative) then weakly compressible $R$-modules are precisely subdirect products of prime $R$-modules if and only if ${\rm dim}(R)=0$ and $R/{\rm N}(R)$ is a semi-Artinian ring if and only if every classical semiprime module is semiprime. In this case, the class of weakly compressible $R$-modules is an enveloping for Mod-$R$. Some related conditions are also investigated.
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참고문헌 (17)
참고문헌 신청
A. Haghany / 2005 / Endoprime modules / Acta Math. Hungar 106 (1-2) : 89 ~ 99
C. Lomp / 2005 / Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions / J. Algebra Appl 4 (1) : 77 ~ 97
E. Enochs / 1993 / The existence of envelopes / Rend. Sem. Mat. Univ. Padova 90 : 45 ~ 51
F. W. Anderson / 1973 / Rings and categories of modules / Springer
H. P. Yu / 1995 / On quasi-duo rings / Glasgow Math. J 37 (1) : 21 ~ 31
C. Lomp / 2005 / Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions / J. Algebra Appl 4 (1) : 77 ~ 97
E. Enochs / 1993 / The existence of envelopes / Rend. Sem. Mat. Univ. Padova 90 : 45 ~ 51
F. W. Anderson / 1973 / Rings and categories of modules / Springer
H. P. Yu / 1995 / On quasi-duo rings / Glasgow Math. J 37 (1) : 21 ~ 31
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