Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 24 Sayı: 24, 1 - 11, 05.07.2018
https://doi.org/10.24330/ieja.440117

Öz

Kaynakça

  • A. J. Diesl, Nil clean rings, J. Algebra, 383 (2013), 197-211.
  • P. A. Freidman, K teorii radikala assotsiativnogo kol'tsa, Izv. V.U.Z. Matematika, 3(4) (1958), 225-232.
  • L. Fuchs, Abelian Groups, Springer Monographs in Mathematics, Springer, Cham, 2015.
  • B. J. Gardner, Torsion classes and pure subgroups, Paci c. J. Math., 33 (1970), 109-116.
  • B. J. Gardner, Elementary radical classes, Int. Electron. J. Algebra, 23 (2018), 25-41.
  • B. J. Gardner and R. Wiegandt, Radical Theory of Rings, Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker, Inc., New York, 2004.
  • G. Gratzer, H. Lakser and J. P lonka, Joins and direct products of equational classes, Canad. Math. Bull., 12 (1969), 741-744.
  • T. K. Hu, Locally equational classes of universal algebras, Chinese J. Math., 1(2) (1973), 143-165.
  • T. Kosan, Z. Wang and Y. Zhou, Nil-clean and strongly nil-clean rings, J. Pure Appl. Algebra, 220(2) (2016), 633-646.
  • N. V. Loi, Essentially closed radical classes, J. Austral. Math. Soc. Ser. A, 35(1) (1983), 132-142.
  • A. I. Mal'tsev, Obumnozhenii klassov algebraicheskikh sistem, Sibirsii Mat. Zh., 8 (1967), 346-365.
  • N. R. McConnell and T. Stokes, Generalising quasiregularity for rings, Austral. Math. Soc. Gaz., 25(5) (1998), 250-252.
  • H. Neumann, Varieties of Groups, Springer-Verlag, New York, Inc., New York, 1967.
  • W. K. Nicholson and Y. Zhou, Clean general rings, J. Algebra, 291(1) (2005), 297-311.
  • P. N. Stewart, Semi-simple radical classes, Paci c. J. Math., 32 (1970), 249- 254.

A NOTE ON MAL'TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES

Yıl 2018, Cilt: 24 Sayı: 24, 1 - 11, 05.07.2018
https://doi.org/10.24330/ieja.440117

Öz

A radical class R of rings is elementary if it contains precisely
those rings whose singly generated subrings are in R. Many examples of ele-
mentary radical classes are presented, and all those which are either contained
in the Jacobson radical class or disjoint from it are described. There is a dis-
cussion of Mal'tsev products of radical classes in general, in which it is shown,
among other things, that a product of elementary radical classes need not be
a radical class, and if it is, it need not be elementary.

Kaynakça

  • A. J. Diesl, Nil clean rings, J. Algebra, 383 (2013), 197-211.
  • P. A. Freidman, K teorii radikala assotsiativnogo kol'tsa, Izv. V.U.Z. Matematika, 3(4) (1958), 225-232.
  • L. Fuchs, Abelian Groups, Springer Monographs in Mathematics, Springer, Cham, 2015.
  • B. J. Gardner, Torsion classes and pure subgroups, Paci c. J. Math., 33 (1970), 109-116.
  • B. J. Gardner, Elementary radical classes, Int. Electron. J. Algebra, 23 (2018), 25-41.
  • B. J. Gardner and R. Wiegandt, Radical Theory of Rings, Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker, Inc., New York, 2004.
  • G. Gratzer, H. Lakser and J. P lonka, Joins and direct products of equational classes, Canad. Math. Bull., 12 (1969), 741-744.
  • T. K. Hu, Locally equational classes of universal algebras, Chinese J. Math., 1(2) (1973), 143-165.
  • T. Kosan, Z. Wang and Y. Zhou, Nil-clean and strongly nil-clean rings, J. Pure Appl. Algebra, 220(2) (2016), 633-646.
  • N. V. Loi, Essentially closed radical classes, J. Austral. Math. Soc. Ser. A, 35(1) (1983), 132-142.
  • A. I. Mal'tsev, Obumnozhenii klassov algebraicheskikh sistem, Sibirsii Mat. Zh., 8 (1967), 346-365.
  • N. R. McConnell and T. Stokes, Generalising quasiregularity for rings, Austral. Math. Soc. Gaz., 25(5) (1998), 250-252.
  • H. Neumann, Varieties of Groups, Springer-Verlag, New York, Inc., New York, 1967.
  • W. K. Nicholson and Y. Zhou, Clean general rings, J. Algebra, 291(1) (2005), 297-311.
  • P. N. Stewart, Semi-simple radical classes, Paci c. J. Math., 32 (1970), 249- 254.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

B. J. Gardner Bu kişi benim

Yayımlanma Tarihi 5 Temmuz 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 24 Sayı: 24

Kaynak Göster

APA Gardner, B. J. (2018). A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES. International Electronic Journal of Algebra, 24(24), 1-11. https://doi.org/10.24330/ieja.440117
AMA Gardner BJ. A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES. IEJA. Temmuz 2018;24(24):1-11. doi:10.24330/ieja.440117
Chicago Gardner, B. J. “A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES”. International Electronic Journal of Algebra 24, sy. 24 (Temmuz 2018): 1-11. https://doi.org/10.24330/ieja.440117.
EndNote Gardner BJ (01 Temmuz 2018) A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES. International Electronic Journal of Algebra 24 24 1–11.
IEEE B. J. Gardner, “A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES”, IEJA, c. 24, sy. 24, ss. 1–11, 2018, doi: 10.24330/ieja.440117.
ISNAD Gardner, B. J. “A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES”. International Electronic Journal of Algebra 24/24 (Temmuz 2018), 1-11. https://doi.org/10.24330/ieja.440117.
JAMA Gardner BJ. A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES. IEJA. 2018;24:1–11.
MLA Gardner, B. J. “A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES”. International Electronic Journal of Algebra, c. 24, sy. 24, 2018, ss. 1-11, doi:10.24330/ieja.440117.
Vancouver Gardner BJ. A NOTE ON MAL’TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES. IEJA. 2018;24(24):1-11.