ON GRADED UJ-RINGS

In this paper, graded rings are $S$-graded rings inducing $S,$ that is, rings whose additive groups can be written as a direct sum of a family of their additive subgroups indexed by a nonempty set $S,$ and such that the product of two homogeneous elements is again a homogeneous element. As a generalization of the recently introduced notion of a $UJ$-ring, we define a graded $UJ$-ring. Graded nil clean rings which are graded $UJ$ are described. We also investigate the graded $UJ$-property under some graded ring constructions.

Keywords:

Graded ring, Jacobson radical nil clean ring,

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G. Calugareanu, UU rings, Carpathian J. Math., 31(2) (2015), 157-163.
M. Chadeyras, Essai d'une theorie noetherienne pour les anneaux commutatifs dont la graduation est aussi generale que possible, Bull. Soc. Math. France Suppl. Mem., 22 (1970), 3-143.
H. Chen, On strongly J-clean rings, Comm. Algebra, 38(10) (2010), 3790-3804.
P. V. Danchev, Rings with Jacobson units, Toyama Math. J., 38 (2016), 61-74.
A. J. Diesl, Nil clean rings, J. Algebra, 383 (2013), 197-211.
E. Halberstadt, Le radical d'un anneide regulier, C. R. Acad. Sci. Paris Ser. A, 270 (1970), 361-363.
E. Halberstadt, Theorie Artinienne Homogene des Anneaux Gradues a Grades Non Commutatifs Reguliers, Ph.D. Thesis, University of Pierre and Marie Currie (Paris VI), Paris, France, 1971.
E. Ilic-Georgijevic, On graded $\Omega$-groups, Filomat, 29(10) (2015), 2167-2183.
E. Ilic-Georgijevic, On graded Brown-McCoy radicals of graded rings, J. Algebra Appl., 15(8) (2016), 1650143 (13 pp).
E. Ilic-Georgijevic, On graded Thierrin radicals of graded rings, Comm. Algebra, 45(9) (2017), 3886-3891.
E. Ilic-Georgijevic, On graded special radicals of graded rings, J. Algebra Appl., 17(6) (2018), 1850109 (10 pp).
E. Ilic-Georgijevic, On radicals of graded ring constructions, in Rings, Modules and Codes, Contemp. Math., Amer. Math. Soc., Providence, RI, 727 (2019), 167-176.
E. Ilic-Georgijevic and S. Sahinkaya, On graded nil clean rings, Comm. Algebra, 46(9) (2018), 4079-4089.
A. V. Kelarev, Combinatorial properties and homomorphisms of semigroups, Internat. J. Algebra Comput., 4(3) (1994), 443-450.
A. V. Kelarev, On groupoid graded rings, J. Algebra, 178 (1995), 391-399.
A. V. Kelarev, Ring Constructions and Applications, Series in Algebra, 9, World Scienti c Publishing Co., Inc., River Edge, NJ, 2002.
A. V. Kelarev and A. Plant, Bergman's lemma for graded rings, Comm. Algebra, 23(12) (1995), 4613-4624.
K. Koh, On lifting idempotents, Canad. Math. Bull., 17(4) (1974), 607.
M. T. Kosan, A. Leroy and J. Matczuk, On UJ-rings, Comm. Algebra, 46(5) (2018), 2297-2303.
M. Krasner, Une generalisation de la notion de corps-corpode, Un corpode remarquable de la theorie des corps values, C. R. Acad. Sci. Paris, 219 (1944), 345-347.
M. Krasner, Anneaux gradues generaux, Algebra Colloquium (Rennes, 1980), Univ. Rennes, Rennes, (1980), 209-308.
W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
W. K. Nicholson and Y. Zhou, Strong lifting, J. Algebra, 285(2) (2005), 795-818.
W. K. Nicholson and Y. Zhou, Clean general rings, J. Algebra, 291(1) (2005), 297-311.

International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

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