Modules which are self-p-injective relative to projection invariant submodules

Kara, Yeliz; Tercan, Adnan

doi:10.1515/auom-2017-0010

Abstract

In this article, we focus on modules M such that every homomorphism from a projection invariant submodule of M to M can be lifted to M. Although such modules share some of the properties of PI -extending (i.e., every projection invariant submodule is essential in a direct summand) modules, it is shown that they form a substantially bigger class of modules.

References

[1] Al-Huzali, A., Jain, S. K., Lopez-Permouth, S. R., On the weak relativeinjectivity of rings and modules, Noncommutative ring theory, Lecture Notes in Math., 1448, Springer, Berlin, 1990.10.1007/BFb0091254
Search in Google Scholar Back to article
[2] Anderson, F. W., Fuller, K. R., Rings and Categories of Modules, New York, Springer-Verlag, 1974.10.1007/978-1-4684-9913-1
Search in Google Scholar Back to article
[3] Birkenmeier, G. F., Tercan, A., Yücel, C. C., The extending condition relative to sets of submodules, Comm. Algebra 42 (2014) 764-778.10.1080/00927872.2012.723084
Open DOI Search in Google Scholar Back to article
[4] Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R., Extending Modules, Pitman, London, 1994.
Search in Google Scholar Back to article
[5] Fuchs, L., Infinite Abelian Groups I, New York, Academic Press, 1970.
Search in Google Scholar Back to article
[6] Guil Asensio, P. A., Sahinkaya, S., Srivastava, A. K., New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture, Isr. J. Math., 214 (2016), 121-148.10.1007/s11856-016-1351-4
Search in Google Scholar Back to article
[7] Jain, S. K., Lopez-Permouth, S. R., A survey on the theory of weakly injective modules, in Computational Algebra, Lecture Notes Pure Appl. Math. 151, Marcel Dekker, New York, (1993) 205-232.10.1201/9781315139975-10
Search in Google Scholar Back to article
[8] Kaplansky, I. Infinite Abelian Groups, University of Michigan Press, 1969.
Search in Google Scholar Back to article
[9] Kara, Y., Tercan, A., Modules whose certain submodules are essentially embedded in direct summands, Rocky Mt. J. Math., 46(2) (2016) 519-532.10.1216/RMJ-2016-46-2-519
Search in Google Scholar Back to article
[10] Lam, T. Y., Lectures on Modules and Rings, Springer-Verlag, 1999.10.1007/978-1-4612-0525-8
Search in Google Scholar Back to article
[11] Mohamed, S. H., Müller, B. J., Continuous and Discrete Modules, London Math. Soc. 147, 1990.10.1017/CBO9780511600692
Search in Google Scholar Back to article
[12] Murthy, M. P., Zero cycles and projective modules, Ann. Math., (1994) 405-434.10.2307/2118605
Search in Google Scholar Back to article
[13] Sandomierski, F.L., Non-singular rings, Proc. Amer. Math. Soc. 19 (1968) 225-230.10.1090/S0002-9939-1968-0219568-5
Open DOI Search in Google Scholar Back to article
[14] Santa-Clara, C., Smith, P. F., Modules which are self-injective relative to closed submodules, Algebra and Its Applications, Contemp. Math., Athens, Ohio, 259 (1999) 487499.
Search in Google Scholar Back to article
[15] Smith, P.F., Tercan, A., Generalizations of CS-modules, Comm. Algebra 21 (1993) 1809-1847.10.1080/00927879308824655
Open DOI Search in Google Scholar Back to article
[16] Smith, P.F., Tercan, A., Continuous and quasi-continuous modules, Houston J. Math., 18(3) (1992) 339-348.
Search in Google Scholar Back to article
[17] Smith, P.F., Tercan, A., Direct summands of modules which satisfy C11, Algebra Colloq., 11 (2004) 231-237.
Search in Google Scholar Back to article
[18] Tercan, A., On certain CS rings, Comm. Algebra 23(2) (1995) 405-419.10.1080/00927879508825228
Open DOI Search in Google Scholar Back to article
[19] Tercan, A., Yücel, C. C., Module Theory, Extending Modules and Generalizations, Basel, Birkhäuser, 2016.10.1007/978-3-0348-0952-8
Search in Google Scholar Back to article

Modules which are self-p-injective relative to projection invariant submodules

Abstract

Paradigm

My account