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Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module $M$, we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by $M$. We also consider the relationship between the conditions (1) $M$ is a fully prime (semiprime) module, and (2) the endomorphism ring of $M$ is a fully prime (semiprime) ring.
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참고문헌 (16)
참고문헌 신청
John A. Beachy / 2002 / M-injective modules and prime M-ideals / Communications in Algebra 30(10):4649~4676
J. A. Beachy / 2019 / Modules which satisfy Gabriel's condition H
L. Bican / 1980 / Prime and coprime modules / Fundamenta Mathematicae 107(1):33~45
William D. Blair / 1994 / Fully prime rings / Communications in Algebra 22(13):5389~5400
Jaime Castro Pérez / 2016 / On Semiprime Goldie Modules / Communications in Algebra 44(11):4749~4768
J. A. Beachy / 2019 / Modules which satisfy Gabriel's condition H
L. Bican / 1980 / Prime and coprime modules / Fundamenta Mathematicae 107(1):33~45
William D. Blair / 1994 / Fully prime rings / Communications in Algebra 22(13):5389~5400
Jaime Castro Pérez / 2016 / On Semiprime Goldie Modules / Communications in Algebra 44(11):4749~4768
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