×
Diallo, Abdoul Djibril; Diop, Papa Cheikhou

Modules whose \(t\)-closed submodules are their homomorphic images. (English) Zbl 1487.16001

J. Discrete Math. Sci. Cryptography 23, No. 6, 1297-1314 (2020).
Summary: In this paper, we introduce the notion of \(t\)-epi-modules. An \(R\)-module \(M\) is called \(t\)-epi if every \(t\)-closed submodule of \(M\) is a homomorphic image of \(M\). Various properties of these modules are studied. Also, connections between \(t\)-epi modules and other related modules are investigated. Finally, quasi-Frobenius rings, right \(t\)-semi-simple rings and right \(\Sigma\)-\(t\)-extending rings are characterized in termes of \(t\)-epi modules.

Cited in 3 Documents

MSC:

16D10 General module theory in associative algebras
16D40 Free, projective, and flat modules and ideals in associative algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16L30 Noncommutative local and semilocal rings, perfect rings

Keywords:

\(t\)-epi modules; \(t\)-closed submodules; epi-retractable modules; regular endomorphisms ring; nonsingular modules
Cite Review PDF
Full Text: DOI

References:

[1] Anderson, F. W.; Fuller, K. R., Rings and category of modules (1973), New York: Springer-Verlag, New York
[2] Asgari, Sh., T-continuous modules, Comm. Algebra, 45, 1941-1952 (2017) · Zbl 1387.16008 · doi:10.1080/00927872.2016.1226868
[3] Asgari, Sh.; Haghany, A., T-extending modules and T-baer modules. (39) 1605-1023, Comm. Algebra (2011) · Zbl 1230.16006 · doi:10.1080/00927871003677519
[4] Asgari, Sh.; Haghany, A., Generalization of T -extending Modules Relative To Fully invariant Submodules, Journal of the Korean Mathematical Society, 49, 3, 503-514 (2012) · Zbl 1258.16008 · doi:10.4134/JKMS.2012.49.3.503
[5] Asgari, Sh.; Haghany, A., T -Rickart modules and Dual T-Rickart modules. (22) 849-870, Algebra Colloquium (2015) · Zbl 1345.16005 · doi:10.1142/S1005386715000735
[6] Asgari, Sh.; Haghany, A.; Tolooei, Y., T -semi-simple modules and T-semi-simple rings, Comm. Algebra, 41, 1882-1902 (2013) · Zbl 1280.16004 · doi:10.1080/00927872.2011.653065
[7] Atani, S. E.; Khoramdel, M.; Hesari, S. D. P., C3-modules, Demostratio Mathematica, 3, 282-292 (2016) · Zbl 1362.16002 · doi:10.1515/dema-2016-0024
[8] Chatters, A. W.; Kheuri, S. M., Endomorphism rings of modules over nonsingular CS rings, J. London Math. Soc, 434-444 (1980) · Zbl 0432.16017
[9] Diallo, A. D.; Diop, P. C.; Barry, M., On C-co-epi-retractable modules, Eur. J. Pure Appl. Maths, 12, 3, 1187-1108 (2019) · Zbl 1438.13012 · doi:10.29020/nybg.ejpam.v12i3.3461
[10] Diallo, A. D.; Diop, P. C.; Barry, M., Some results on c-retractable modules, Eur. J. Pure Appl. Maths, 13, 1, 158-169 (2020) · doi:10.29020/nybg.ejpam.v13i1.3588
[11] Hamdouni, A.; Ozcan, A. C.; Harmanci, A., Charcterizations of modules and rings by the summand intersection property and the summand sum property, JP J. Algebra Number Theory Appl, 3, 469-490 (2005) · Zbl 1150.16004
[12] Huynh, D. V.; Rizvi, S. T., An approche to Boyle’s conjecture, Proceeding of the Edinburg, Math. Society, 267-273 (1997) · Zbl 0885.16002 · doi:10.1017/S0013091500023713
[13] Dung, N. V.; Huynh, D. V.; Smith, P. F.; Wisbauer, R., Extending modules, Pitman Research Notes in Mathematics 313 (1994), Harlow: Longman, Harlow · Zbl 0841.16001
[14] Ghorbani, A.; Vedadi, M. R., Epi-retractable modules and some application, Bull. Iranian Math. Soc., 35, 1, 155-166 (2009) · Zbl 1197.16005
[15] Kheury, S. M., The endomorphism ring of nonsingular retractable modules East-West, J. Math., 2, 2, 161-170 (2000) · Zbl 0988.16020
[16] Lam, T. Y., Lectures on modules and rings, G.T.M.(189) (1999), Springer-Verlag, Berlin-Heidelber: Springer-Verlag, Berlin-Heidelber, New York · Zbl 0911.16001
[17] Lee, G., Theory of Rickart modules, Ph. D. Thesis, M.S., Graduate, School of the Ohio State University (2010).
[18] Mohamed, S. H.; Muller, B. J., Continuous and Discrete Modules, LMS Lecture Note Series, 147 (1990), Cambridge University Press: Cambridge University Press, Cambridge · Zbl 0701.16001
[19] Mostafanasab, H., Applications of Epi-retractable and Co-epi-retractable modules, Bull. Iranian Math. Soc., 38, 5, 903-917 (2013) · Zbl 1307.16001
[20] Nicholson, W. K.; Yousif, M., Quasi-Frobenius rings, Cambridge Tracts in Mathematics 158 (2003), Cambridge University Press · Zbl 1042.16009
[21] Pandeya, B. M.; Chaturvedi, A. K.; Gupta, A. J., Application of episretractable modules, Bull. Iranian Math. Soc, 38, 2, 469-477 (2012) · Zbl 1300.16008
[22] Rizvi, S. T.; Roman, C. S., On K-nonsinglar modules and applications, Comm. Algebra, 35, 2960-2980 (2007) · Zbl 1154.16005 · doi:10.1080/00927870701404374
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.