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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2010.1
- 수록면
- 101 - 107 (7page)
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A module M is said to satisfy the EC11 condition if every ec-submodule of M has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the EC11 and P-extending conditions are equivalent. It is shown that the EC11 property is not inherited by direct summands. Moreover, we prove that if M is an EC11-module where SocM is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.
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참고문헌 (15)
참고문헌 신청
B. Stenstrom / 1975 / Rings of Quotients / Springer-Verlag
C. Celep Yucel / 2009 / Modules whose ec-closed submodules are direct sum- mand / Taiwanese J. Math. 13 : 1247 ~ 1256
F. Tak l / 2009 / Modules whose submodules essentially embedded in direct sum- mands / Comm. Algebra 37 : 460 ~ 469
F.W. Anderson / 1992 / Rings and Catogories of Modules / Springer-Verlag
G.F. Birkenmeier / 1999 / When is the CS condition hereditary? / Comm. Algebra 27 (8) : 3875 ~ 3885
C. Celep Yucel / 2009 / Modules whose ec-closed submodules are direct sum- mand / Taiwanese J. Math. 13 : 1247 ~ 1256
F. Tak l / 2009 / Modules whose submodules essentially embedded in direct sum- mands / Comm. Algebra 37 : 460 ~ 469
F.W. Anderson / 1992 / Rings and Catogories of Modules / Springer-Verlag
G.F. Birkenmeier / 1999 / When is the CS condition hereditary? / Comm. Algebra 27 (8) : 3875 ~ 3885
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