On Weak Projection Invariant Semisimple Modules

ISSN: 2645-8845
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2018
Yayıncı: Fuat USTA

We introduce and investigate the notion of weak projection invariant semisimple modules. We deal with the structural properties of this new class of modules. In this trend we have indecomposable decompositions of the special class of the former class of modules via some module theoretical properties. As a consequence, we obtain when the finite exchange property implies full exchange property for the latter class of modules.

Keywords:

Exchange property, Extending module Projection invariant submodule,

PDF

___

[1] N. V. Dung, D. V. Huynh, P. F. Smith, R. Wisbauer, Extending Modules, Longman, Harlow, 1994.
[2] F. T. Mutlu, On matrix rings with the SIP and the Ads, Turk. J. Math., 42 (2018), 2657 – 2663.
[3] A. Tercan, C. C. Y¨ucel, Module theory extending modules and generalizations, Birkhauser, Basel, 2016.
[4] R. Yasşar, Modules in which semisimple fully invariant submodules are essential in summands, Turk. J. Math., 43(5) (2019), 2327-2336.
[5] G. F. Birkenmeier, Y. Kara, A. Tercan, p-Baer rings, J. Algebra App., 17(2) (2018), 1850029.
[6] G. F. Birkenmeier, A. Tercan, C. C. Y¨ucel, The extending condition relative to sets of submodules, Comm. Algebra, 42 (2014), 764-778.
[7] Y. Kara, On projective invariant semisimple submodules, Al-Qadisiyah J. Pure Sci., 26(1) (2020), 13-19.
[8] B. Zimmermann, W. Zimmermann, Classes of modules with the exchange property, J. Algebra, 88(2) (1984), 416-434.
[9] S. H. Mohamed, B. J. M¨uller, Continuous and Discrete Modules, Cambridge University Press, 1990.
[10] G. F. Birkenmeier, J. K. Park, S. T. Rizvi, Extensions of rings and modules, Birkhauser, New York, NY, USA, 2013.
[11] L. Fuchs, Infinite Abelian Groups I, Academic Press, New York, NY, USA, 1970.
[12] A. Tercan, Weak (C11) modules and algebraic topology type examples, Rocky Mount J. Math., 34(2) (2004), 783-792.
[13] I. Kaplansky, Rings of Operators, Benjamin, New York, NY, USA, 1968.