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2018 | 72 | 1 |
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Invo-regular unital rings

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo-Khurana (Comm. Algebra, 2001), recently Nielsen and Ster showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017.
Rocznik
Tom
72
Numer
1
Opis fizyczny
Daty
wydano
2018
online
2018-06-25
Twórcy
Bibliografia
  • Camillo, V. P., Khurana, D., A characterization of unit regular rings, Commun. Algebra 29 (2001), 2293-2295.
  • Danchev, P. V., A new characterization of Boolean rings with identity, Irish Math. Soc. Bull. 76 (2015), 55-60.
  • Danchev, P. V., On weakly clean and weakly exchange rings having the strong property, Publ. Inst. Math. Beograd 101 (2017), 135-142.
  • Danchev, P. V., Invo-clean unital rings, Commun. Korean Math. Soc. 32 (2017), 19-27.
  • Danchev, P. V., Lam, T. Y., Rings with unipotent units, Publ. Math. Debrecen 88 (2016), 449-466.
  • Ehrlich, G., Unit-regular rings, Portugal. Math. 27 (1968), 209-212.
  • Goodearl, K. R., Von Neumann Regular Rings, Second Edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1991.
  • Hartwig, R. E., Luh, J., A note on the group structure of unit regular ring elements, Pacific J. Math. 71 (1977), 449-461.
  • Hirano, Y., Tominaga, H., Rings in which every element is the sum of two idempotents, Bull. Austral. Math. Soc. 37 (1988), 161-164.
  • Lam, T. Y., A First Course in Noncommutative Rings, Second Edition, Springer-Verlag, Berlin-Heidelberg-New York, 2001.
  • Lam, T. Y., Murray, W., Unit regular elements in corner rings, Bull. Hong Kong Math. Soc. 1 (1997), 61-65.
  • Nicholson, W. K., Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278.
  • Nicholson, W. K., Strongly clean rings and Fitting’s lemma, Commun. Algebra 27 (1999), 3583-3592.
  • Nielsen, P. P., Ster, J., Connections between unit-regularity, regularity, cleanness and strong cleanness of elements and rings, Trans. Amer. Math. Soc. 370 (2018), 1759-1782.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_45-53
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