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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Proceedings of the Jangjeon Mathematical Society Proceedings of the Jangjeon Mathematical Society Vol.20 No.4
- 발행연도
- 2017.1
- 수록면
- 595 - 604 (10page)
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초록· 키워드
오류제보하기
Let R be an associative ring with identity and Spec(M) denote the set of all prime submodules of a right R-module M. In this paper, we study the classical Zariski topology on Spec(M) which is denoted by Τc. We prove that if (Spec(M), Τc) is a Noetherian topological space, then M has
nitely many minimal prime submodules. We characterize all the irreducible components of (Spec(M), Τc) and all the minimal prime submodules of M for a non-zero at module M over a commutative ring R. We obtain some results concerning compactness and connectedness of (Spec(M), Τc) by using algebraic properties of the module M. We give some equivalent conditions for (Spec(M), Τc) to be a Hausdor¤ space or T1-space when M is a right module over a left perfect ring R.
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참고문헌 (13)
참고문헌 신청
A. Abbasi / 2012 / Modules and spectral spaces / Comm. Algebra 40(11):4111~4129
Ansari-Toroghy, H. / 2010 / On the prime spectrum of a module and zariski topologies / Comm. Algebra 38:4461~4475
M. Behboodi / 2008 / Classical Zariski Topology of Modules and Spectral Spaces I / Inter. Electronic J. Alg 4:104~130
M. Behboodi / 2008 / Classical Zariski Topology of Modules and Spectral Spaces II / Inter. Electronic J. Alg 4:131~148
S. Çeken / 2013 / Second modules over noncommutative rings / Communications in Algebra 41(1):83~98
Ansari-Toroghy, H. / 2010 / On the prime spectrum of a module and zariski topologies / Comm. Algebra 38:4461~4475
M. Behboodi / 2008 / Classical Zariski Topology of Modules and Spectral Spaces I / Inter. Electronic J. Alg 4:104~130
M. Behboodi / 2008 / Classical Zariski Topology of Modules and Spectral Spaces II / Inter. Electronic J. Alg 4:131~148
S. Çeken / 2013 / Second modules over noncommutative rings / Communications in Algebra 41(1):83~98
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