| | | |

Simple continuous modules

Yongduo WANG [1]

A module $M$ is called a simple continuous module if it satisfies the conditions $(min-C_{1})$ and $(min-C_{2})$. A module $M$ is called singular simple-direct-injective if for any singular simple submodules $A$, $B$ of $M$ with $A\cong B\mid M$, then $A\mid M$. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple continuous modules and singular simple-direct-injective modules. For instance, it is shown that a ring $R$ is a right $V$-ring if and only if every right $R$-module is a simple continuous modules, and that a regular ring $R$ is a right $GV$-ring if and only if every cyclic right $R$-module is a singular simple-direct-injective module.
simple continuous module, singular simple-direct-injective module, $V$-ring, $GV$-ring
• [1] I. Amin, Y. Ibrahim and M.F. Yousif, C3-modules, Algebra Colloq. 22, 655-670, 2015.
• [2] I. Amin, M.F. Yousif and N. Zeyada, Soc-injective rings and modules, Comm. Algebra 33, 4229-4250, 2005.
• [3] F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, Berlin, New York, 1974.
• [4] J.-E. Björk, Rings satisfying certain chain conditions, J. Reine Angew. Math. 245, 63-73, 1970.
• [5] V. Camillo, Y. Ibrahim, M.F. Yousif and Y.Q. Zhou, Simple-direct-injective modules, J. Algebra 420, 39-53, 2014.
• [6] J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Birkhäuser Basel, 2006.
• [7] N.V. Dung, D.V. Huynh, P.F. Smith and R. Wisbauer, Extending Modules, Longman Scientific and Technical, 1994.
• [8] C. Faith, Algebra II: Ring Theory, Springer-Verlag, Berlin, New York, 1976.
• [9] J.W. Fisher, Von Neumann regular rings versus V-rings, in: Lect. Notes Pure Appl. Math. 7, 101-119, Dekker, New York, 1974.
• [10] F. Kasch, Modules and Rings, London Math. Soc. Monogr. 17, Academic Press, New York, 1982.
• [11] S.H. Mohamed and B.J. Müller, Continuous and Discrete Modules, Cambridge Univ. Press, Cambridge, UK, 1990.
• [12] W.K. Nicholson and M.F. Yousif, Quasi-Frobenius Rings, Cambridge Tracts in Math. 158, Cambridge Univ. Press, Cambridge, UK, 2003.
• [13] A.C. Özcan, A. Harmanci and P.F. Smith, Duo modules, Glasgow Math. J. 48, 533- 545, 2006.
• [14] V.S. Ramamurthi and K.M. Rangaswamy, Generalized V -rings, Math. Scand. 31, 69-77, 1972.
• [15] P.F. Smith, CS-modules and Weak CS-modules, Non-commutative Ring Theory, 99- 115, Springer LNM 1448, 1990.
• [16] P.F. Smith, Modules for which every submodule has a unique closure, in: Ring Theory, 303-313, World Scientific, Singapore, 1993.
• [17] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadel- phia, 1991.
Birincil Dil en Matematik Matematik Orcid: 0000-0002-0756-3899Yazar: Yongduo WANG (Sorumlu Yazar) Yayımlanma Tarihi : 8 Ekim 2019
 Bibtex @araştırma makalesi { hujms629829, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1336 - 1344}, doi = {}, title = {Simple continuous modules}, key = {cite}, author = {Wang, Yongduo} } APA Wang, Y . (2019). Simple continuous modules . Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1336-1344 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629829 MLA Wang, Y . "Simple continuous modules" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1336-1344 Chicago Wang, Y . "Simple continuous modules". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1336-1344 RIS TY - JOUR T1 - Simple continuous modules AU - Yongduo Wang Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1336 EP - 1344 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Simple continuous modules %A Yongduo Wang %T Simple continuous modules %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U ISNAD Wang, Yongduo . "Simple continuous modules". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1336-1344 . AMA Wang Y . Simple continuous modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1336-1344. Vancouver Wang Y . Simple continuous modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1336-1344.

Makalenin Yazarları