On a Generalized Semicommutative Ring
Main Article Content
Abstract
Let R be a ring with identity. In this paper, we introduce some new results in a class of rings which refers to generalization of semicommutative rings called Q-semicommutative rings whenever x2=0 implies xRx=0, for any a ∈R [7]. They study investigates general properties of Q-semicommutative rings and shows several results of semicommutative ring can be extended to Q-semicommutative rings
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] H.E. Bell, (1970). "Near rings in which each element is a power of it self", Bull Austral . Math. Soc.2,363-368 .
[2] G. Shin, (1973). "Prime ideals and sheaf representation of a pseudo symmetric rings", Trans. Amer. Math. Soc. 184.
[3] NamKyun Kima;∗, Yang Leeb, (2003). "Extensions of reversible rings", Journal of Pure and Applied Algebra 185 207 – 223.
[4] G. Marks, (2003). " A taxonomy of 2-premal ring", Journal of Algebra 266 494–520 .
[5] Kyung-Yuen Ham, Young Cheol Jeon, Jinwoo Kang, Nam Kyun Kim,Wonjae Lee, Yang Lee, Sung Ju Ryu, and Hae- Hun Yang, (2008). "IFP RINGS AND NEAR-IFP RINGS", J. Korean Math. Soc. 45, No. 3, pp. 727–740.
[6] P.M. Cohn, (1999). "Reversible rings", Bull London Math. Soc. 31,641-648 .
[7] Li Liang, Limin Wang and Zhongkui Liu,( 2007). "ON A GENERALIZATION OF SEMICOMMUTATIVE RINGS", TAIWANESE JOURNAL OF MATHEMATICS, Vol. 11, No. 5, pp. 1359-1368, December .
[8] EBEN MATLIS, (1985). "Commutative Semi-coherent a Semi-regular Rings", JOURNAL OF ALGEBRA 95, 343-372.
[9] Thomas W. Hungerford, Graduate Texts in Mathematics, © 1974 Springer-Verlag New York, Inc.
[10] M.F. ATIYAH, FRS, I.G MACDONALD, (1969). "Introduction to Commutative Algebra", copyright© by Addison-Wesley publishing company, Inc.
[11] Shu-Hao Sun, (1991). "Noncom mutative rings in which every prime is unique maximal ideal", Journal of Pure and Applied Algebra 76 179-192.
[12] HONG KEE KIM, NAM KYUN KIM, MUN SEOB JEONG, YANG LEE, SUNG JURYU, AND DONG EUN YEO, (2009). "ON CONDITIONS PROVIDED BY NILRADICALS', J. Korean Math. Soc. 46, No. 5, pp. 1027-1040 .
[13] Nam Kyun Kimaa,*, Yang Leebb,*, (2002). "On rings whose prime ideals are completely prime", Journal of Pure and applied Algebra 170 255–265.
[14] C. SELVARAJ1,a AND S. PETCHIMUTHU1,b ,(2011). "ON PRIME SPECTRUMS OF 2-PRIMAL RINGS", Bulletin of the Institute of Mathematics, Academia Sonica (New Series), Vol. 6, No. 1, pp. 73-84 .
[15] M.Behboodi*,** and G.Behboodi Eskandari,( 2015). "LOCAL DUO RINGS WHOSE FINITELY GENERATED MODULES ARE DIRECT SUMS OF CYCLIC", Indian J.Pure Appl. Math.,46(1):59-72,February © Indian National science Academy .
[16] Victor Camillo, Pace P. Nielsen, (2008)."McCoy ring and zero- divisors", Journal of Pure and Appl. Algebra 212 599-615.
[17] pace P. Nielsen,( 2006). "Semicommutative and The McCoy condition", Journal of Algebra, vol.298 (2) p.134-141 .
[18] K.R. Goodearl,( 1991). "Von Neumann Regular Rings", Krieger Pub. Co. .
[19] SEO UN HWANG, YANG LEE AND KWANG SUG PARK, (2007). "ON STRONGLY 2-PRIMAL RING", Honan Mathematical J.29, No. 4, pp. 555-567 .
[20] G.F. Birkenmeier, H.E. Heathery and Enoch K. Lee,(1992). "Completely prime ideals and associated radicals", Proc. Biennial Ohio State-Denison Conf. (World Scientific.New Jersey, 1993) 102-129.
[21]Chan Yong Hong & Tai Keen Kwan, (2000) . "On minimal strongly prime ideals", COMMUNICATION IN ALGEBRA, 28(10),4867- 4878.
[22] Chan Huh,1 Yang Lee,1,* and Agate Smoktunowicz2, (2002). " ARMENDARIZ RINGS AND SEMICOMMUTATIVE RING", COMMUNICATION IN ALGEBRA, 30(2), 751-761.