(Co)retractability and (Co)Semi-potency
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module $M$ whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.
Abstract
This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module $M$ whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.
참고문헌 (10)
- A. N. Abyzov, "Io Modules", Mat. Zametki, 08, pp.1~17 (2014)
- B. Amini, "Co-retractable modules", J. Aust. Math. Soc, 86(3), pp.289~304 (2009)
- A. Haghany, "Study of semi-projective retractable modules", Algebra Colloquium, 14(3), pp.489~496 (2007)
- H. Hamza, "Io Rings and Io Modules", Math. J. Okayama Univ, 40, pp.91~97 (1998)
- F. Kasch, "Rings, Modules, and the Total, Front. Math" (2004), Birkhauser Verlag
- W. K. Nicholson, "Io Rings", Trans. Amer. Math. Soc, 207, pp.361~373 (1975)
- H. Tansee, "A Note on Semi-Projective Modules", Kyungpook Mathematical Journal, 42(2), pp.369~380 (2002), 경북대학교 자연과학대학 수학과
- A. A. Tuganbaev, "Rings over which all modules are Io modules", Fundam. Prikl. Mat, 13, pp.185~194 (2007)
- R. Ware, "Endomorphism rings of projective modules", Trans. Amer. Math. Soc, 155, pp.233~256 (1971)
- R. Wisbauer, "Foundations of Modules and Rings Theory" (1991), Gordon and Breach