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A characterization of weakly J(n)-rings

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Języki publikacji
EN
Abstrakty
EN
A ring R is called a J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equality r (n+1) = r holds and a weakly J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equalities r (n+1) = r or r(n+1) = -r hold. We completely describe both classes of these rings R for any n, thus considerably extending some well-known results in the subject, especially that of V. Perić in Publ. Inst. Math. Beograd (1983) as well as, in particular, the classical description of Boolean rings when n = 1.
Rocznik
Tom
Strony
53--61
Opis fizyczny
Bibliogr. 17 poz..
Twórcy
  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, "Acad. G. Bonchev" str., bl. 8, 1113 Sofia, Bulgaria
Bibliografia
  • [1] R.F. Arens, I. Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948) 457-481.
  • [2] G. Birkhoff, M. Ward, A characterization of Boolean algebras, Ann. Math. 40 (1939) 609-610.
  • [3] T. Chinburg, M. Henriksen, Multiplicatively periodic rings, Amer. Math. Monthly 83 (1976) 547-549.
  • [4] P.V. Danchev, Weakly semi-boolean unital rings, JP J. Algebra Num. Theory & Appl. 39 (2017) 261-276.
  • [5] P.V. Danchev, Weakly tripotent rings, Kragujevac J. Math. 43 (2019) 465-469.
  • [6] P.V. Danchev, Weakly quadratent rings, J. Taibah Univ. Sci. 13 (2019) 121-123.
  • [7] P.V. Danchev, T.Y. Lam, Rings with unipotent units, Publ. Math. Debrecen 88 (2016) 449-466.
  • [8] P. Danchev, J. Matczuk, n-Torsion clean rings, Contemp. Math. (2019).
  • [9] P.V. Danchev, W.Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra 425 (2015) 410-422.
  • [10] D.E. Dobbs, J.O. Kiltinen, B.J. Orndor, Commutative rings with homomorphic power functions, Internat. J. Math. and Math. Sci. 15 (1992) 91-102.
  • [11] Y. Hirano, H. Tominaga, Rings in which every element is the sum of two idempotents, Bull. Austral. Math. Soc. 37 (1988) 161-164.
  • [12] N. Jacobson, Structure theory for algebraic algebras of bounded degree, Ann. Math. 46 (1945) 695-707.
  • [13] T.-K. Lee, Y. Zhou, From boolean rings to clean rings, Contemp. Math. 609 (2014) 223-232.
  • [14] J. Luh, On the structure of J-rings, Amer. Math. Monthly 74 (1967) 164-166.
  • [15] N.H. McCoy, D. Montgomery, A representation of generalized Boolean rings, Duke Math. J. 3 (1937) 455-459.
  • [16] W.K. Nicholson, Strongly clean rings and Fitting's lemma, Commun. Algebra 27 (1999) 3583-3592.
  • [17] V. Perić, On rings with polynomial identity xn - x = 0, Publ. Inst. Math. (Beograd) (N.S.) 34 (48) (1983) 165-168.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-57a6a294-5637-4855-a078-3a205ce24369
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