Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
amalgamated algebra; nil-clean ring; periodic ring; pullback; UU ring; semiclean ring
Summary:
This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
References:
[1] Anderson, D. D., Bisht, N.: A generalization of semiclean rings. Commun. Algebra 48 (2020), 2127-2142. DOI 10.1080/00927872.2019.1710177 | MR 4085783 | Zbl 1440.16043
[2] Arora, N., Kundu, S.: Semiclean rings and rings of continuous functions. J. Commut. Algebra 6 (2014), 1-16. DOI 10.1216/JCA-2014-6-1-1 | MR 3215558 | Zbl 1294.16025
[3] Badawi, A.: On abelian $\pi$-regular rings. Commun. Algebra 25 (1997), 1009--–1021. DOI 10.1080/00927879708825906 | MR 1437658 | Zbl 0881.16003
[4] Badawi, A., Chin, A. Y. M., Chen, H. V.: On rings with near idempotent elements. Int. J. Pure Appl. Math. 1 (2002), 255-261. MR 1912681 | Zbl 1008.16007
[5] Bakkari, C., Es-Saidi, M.: Nil-clean property in amalgamated algebras along an ideal. Ann. Univ. Ferrara Sez. VII Sci. Mat. 65 (2019), 15-20. DOI 10.1007/s11565-018-0304-8 | MR 3941129 | Zbl 1441.13036
[6] Bell, H. E.: On quasi-periodic rings. Arch. Math. 36 (1981), 502-509. DOI 10.1007/BF01223732 | MR 1552710 | Zbl 0443.16016
[7] Chacron, M.: On a theorem of Herstein. Can. J. Math. 21 (1969), 1348-1353. DOI 10.4153/CJM-1969-148-5 | MR 0262295 | Zbl 0213.04302
[8] Chhiti, M., Mahdou, N., Tamekkante, M.: Clean property in amalgamated algebras along an ideal. Hacet. J. Math. Stat. 44 (2015), 41-49. DOI 10.15672/HJMS.2015449103 | MR 3363762 | Zbl 1320.13020
[9] D'Anna, M., Finocchiaro, C. A., Fontana, M.: Amalgamated algebras along an ideal. Commutative Algebra and Its Applications Walter de Gruyter, Berlin (2009), 155-172. DOI 10.1515/9783110213188.155 | MR 2606283 | Zbl 1177.13043
[10] Diesl, A. J.: Nil clean rings. J. Algebra 383 (2013), 197-211. DOI 10.1016/j.jalgebra.2013.02.020 | MR 3037975 | Zbl 1296.16016
[11] Han, J., Nicholson, W. K.: Extensions of clean rings. Commun. Algebra 29 (2001), 2589-2595. DOI 10.1081/AGB-100002409 | MR 1845131 | Zbl 0989.16015
[12] Hirano, Y., Tominaga, H., Yaqub, A.: On rings in which every element is uniquely expressible as a sum of a nilpotent element and a certain potent element. Math. J. Okayama Univ. 30 (1988), 33-40. DOI 10.18926/mjou/33546 | MR 0976729 | Zbl 0665.16016
[13] Huckaba, J. A.: Commutative Rings with Zero-Divisors. Monographs and Textbooks in Pure and Applied Mathematics 117. Marcel Dekker, New York (1988). MR 0938741 | Zbl 0637.13001
[14] Kabbaj, S.-E.: Matlis' semi-regularity and semi-coherence in trivial ring extensions: A survey. (to appear) in Moroccan J. Algebra Geometry Appl.
[15] Kabbour, M.: Trivial ring extensions and amalgamations of periodic rings. Gulf J. Math. 3 (2015), 12-16. MR 3339429 | Zbl 1389.13053
[16] Mahdou, N., Moutui, M. A. S.: On $(A)$-rings and strongly $(A)$-rings issued from amalgamation. Stud. Sci. Math. Hung. 55 (2018), 270-279. DOI 10.1556/012.2018.55.2.1397 | MR 3813356 | Zbl 1413.13019
[17] Mahdou, N., Moutui, M. A. S.: Gaussian and Prüfer conditions in bi-amalgamated algebras. Czech. Math. J. 70 (2020), 381-391. DOI 10.21136/CMJ.2019.0335-18 | MR 4111849 | Zbl 7217141
[18] Mahdou, N., Moutui, M. A. S.: Prüfer property in amalgamated algebras along an ideal. Ric. Mat. 69 (2020), 111-120. DOI 10.1007/s11587-019-00451-1 | MR 4098175 | Zbl 1440.13088
[19] McGovern, W. W., Raphael, R.: Considering semi-clean rings of continuous functions. Topology Appl. 190 (2015), 99-108. DOI 10.1016/j.topol.2015.05.001 | MR 3349509 | Zbl 1322.46020
[20] Nicholson, W. K.: Lifting idempotents and exchange rings. Trans. Am. Math. Soc. 229 (1977), 269-278. DOI 10.1090/S0002-9947-1977-0439876-2 | MR 0439876 | Zbl 0352.16006
[21] Ôhori, M.: On strongly $\pi$-regular rings and periodic rings. Math. J. Okayama Univ. 27 (1985), 49-52. MR 0833455 | Zbl 0598.16019
[22] Šter, J.: Corner rings of a clean ring need not be clean. Commun. Algebra 40 (2012), 1595-1604. DOI 10.1080/00927872.2011.551901 | MR 2924469 | Zbl 1247.16034
[23] Ye, Y.: Semiclean rings. Commun. Algebra 31 (2003), 5609-5625. DOI 10.1081/AGB-120023977 | MR 2005247 | Zbl 1043.16015
Partner of
EuDML logo