Semiregular and Weakly Regular Rings
For a module M, we say that a submodule N of M lies above a direct summand of M if there is a direct decomposition M = P⊕Q such that P⊆N and Q⋂N is a superfluous submodule of Q. In this case, Q⋂N is a superfluous submodule of M and Q⋂N⊆J(M).
KeywordsDirect Summand Regular Ring Cyclic Module Direct Decomposition Semiprime Ring
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