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On lifting Baer modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 2، اسفند 2023، صفحه 127-133 اصل مقاله (277.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.23345.1466 | ||
| نویسندگان | ||
| Y. Talebi* 1؛ F. Bakhshandeh2 | ||
| 1Department of Mathematics, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Mathematics, University of Mazandaran, Babolsar, Iran | ||
| چکیده | ||
| We introduce the notion of lifting Baer modules, as a generalization of both Baer and lifting modules and give some of their properties. A module $M$ is called lifting Baer if right annihilator of a left ideal of ${\rm End}(M)$ lies above a direct summand of M. Also, we define the concepts of $r$-supplemented and amply $r$-supplemented modules. It is shown that an amply $r$-supplemened module M that every supplement submodule, is a direct summand of $M$, is lifting Baer. The relationships between Baer modules and lifting Baer modules are investigated. Morever, we prove that the endomorphism ring of any lifting Baer module is lifting Baer ring. | ||
| کلیدواژه‌ها | ||
| lifting Baer module؛ Baer module؛ lifting module؛ Annihilators؛ Endomorphism rings | ||
| مراجع | ||
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1. J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Frontiers in Mathematics, Birkauser Verlag, 2006. 2. I. Kaplansky, Rings of Operators, Math. Lecture Note Ser., New York, 1968. 3. D. Keskin Tutuncu and R. Tribak, On -noncosingular modules, Bull. Austral. Math. Soc., 80 (2009), 462-471. 4. S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge, University Press, 1990. 5. S. T. Rizvi and C. S. Roman, Baer and Quasi-Baer Modules, Comm. Algebra. 32 (2004), 103-123. 6. S. T. Rizvi and C. S. Roman, On direct sums of Baer module , J. Algebra, (2) 321 (2009), 682-696. 7. R. Wisbauer, Foundations of Modules and Ring Theory , Gordon & Breach , Reading, 1991. | ||
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آمار تعداد مشاهده مقاله: 123 تعداد دریافت فایل اصل مقاله: 179 |
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