On dual \(\pi\)-endo Baer modules

Yeliz Kara

doi:10.26637/mjm0902/005

Abstract

We introduce the concept of dual \(\pi\)-endo Baer modules. We evolve several structural properties such as direct summands and direct sums. Moreover, we prove that the endomorphism ring of a dual \(\pi\)-endo Baer module is a \(\pi\)-Baer ring. The examples are presented to exhibit the results.

Keywords:

Baer ring, \(\pi\)-Baer ring, dual-Baer module, projection invariant submodule, endomorphism ring

Mathematics Subject Classification:

16D10 , 16D80

Authors Imprint References Funding Related Articles Downloads

Yeliz Kara Department of Mathematics, Bursa Uludag University, 16059, Bursa, Turkey.

Pages: 39-45
Date Published: 01-04-2021
Vol. 9 No. 02 (2021): Malaya Journal of Matematik (MJM)

B. AMINI, M. ERSHAD, H. SHARIF, Coretractable modules, J. Aust. Math. Soc., 86(2009), 289-304.

https://doi.org/10.1017/S1446788708000360

T. AMOUZEGAR, Y. TALEBI, On quasi-dual Baer modules, TWMS J. Pure Appl. Math., 4(1)(2013), 78-86.

F. W. ANDERSON, K.R. FULLER, Rings and Categories of Modules, Springer-Verlag, New York, (1992).

https://doi.org/10.1007/978-1-4612-4418-9

G.F. BIRKENMEIER, Y. KARA, A. TERCAN, π-Baer rings, J. Algebra Appl. 17(2)(2018), 1850029 19 pages.

https://doi.org/10.1142/S0219498818500299

G.F. BIRKENMEIER, Y. KARA, A. TERCAN, π-Endo Baer modules, Commun. Algebra, 48(3)(2020), 1132- 1149.

https://doi.org/10.1080/00927872.2019.1677690

G.F. BIRKENMEIER, J.K. PARK, S.T. RIZVI, Extensions of Rings and Modules, Birkha¨user, New York, (2013).

https://doi.org/10.1007/978-0-387-92716-9

G.F. BIRKENMEIER, A. TERCAN, C.C. YU¨ CEL, The extending condition relative to sets of submodules, Commun. Algebra, 42(2014), 764-778.

https://doi.org/10.1080/00927872.2012.723084

W.E. CLARK, Twisted matrix units semigroup algebras. Duke Math. J. 34(1967), 417-423.

https://doi.org/10.1215/S0012-7094-67-03446-1

K.R. GOODEARL, Simple Noetherian rings the Zalesskii-Neroslavskii examples, Ring Theory Waterloo 1978 Proceedings, Lecture notes in Mathematics., 734(1979), 118-130.

https://doi.org/10.1007/BFb0103156

I. KAPLANSKY, Rings of Operators, New York, Benjamin, (1968).

D. KESKIN TU¨ TU¨ NCU¨ , P.F. SMITH, S.E. TOKSOY, On dual Baer modules, Contemporary Math. 609(2014), 173-184.

https://doi.org/10.1090/conm/609/12081

D. KESKIN TU¨TU¨NCU¨R. TRIBAK, On dual Baer modules, Glasgow Math. J., 52(2010), 261-269.

https://doi.org/10.1017/S0017089509990334

T.Y. LAM, Lectures on Modules and Rings, Springer, Berlin (1999).

https://doi.org/10.1007/978-1-4612-0525-8

S.T. RIZVI, C.S. ROMAN, Baer and Quasi-Baer modules, Commun. Algebra 32(2004), 103-123.

https://doi.org/10.1081/AGB-120027854