Research Article
BibTex RIS Cite
Year 2023, , 87 - 95, 31.07.2023
https://doi.org/10.54974/fcmathsci.1203544

Abstract

References

  • Aydın N., Demir C., Camcı D.K., The source of semiprimeness of rings, Communications of the Korean Mathematical Society, 33(4), 1083-1096, 2018.
  • Barnes W., On the Γ -rings of Nobusawa, Pacific Journal of Mathematics, 18(3), 411-422, 1966.
  • Coppage W.E., Luh J., Radicals of gamma rings, Journal of the Mathematical Society of Japan, 23(1), 40-52, 1971.
  • Kandamar H., The k-derivation of a Gamma-ring, Turkish Journal of Mathematics, 23(3), 221-229, 2000.
  • Kyuno S., On the radicals of Γ-rings, Osaka Journal of Mathematics, 12(3), 639-645, 1975.
  • Kyuno S., On prime gamma rings, Pacific Journal of Mathematics, 75(1), 185-190, 1978.
  • Kyuno S., Gamma Rings, Hadronic Press, Inc., 1991.
  • Kyuno S., A gamma ring with minimum conditions, Tsukuba Journal of Mathematics, 5(1), 47-65, 1981.
  • Luh J., On the theory of simple Γ-rings, The Michigan Mathematical Journal, 16(1), 65-75, 1969.
  • McCoy N.H., The Theory of Rings, MacMillan, 1968.
  • Nobusawa N., On a generalization of the ring theory, Osaka Journal of Mathematics, 1(1), 81-89, 1964.

The Source of Semi-Primeness of Γ-Rings

Year 2023, , 87 - 95, 31.07.2023
https://doi.org/10.54974/fcmathsci.1203544

Abstract

The notion of source of semi-primeness is firstly given by Aydın, Demir and Camcı in 2018 as
the set of all elements a of R that satisfy aRa 􀀀 0 for any associative ring R. They investigated some
basic properties of this set and defined three types of rings which have not appeared in literature before.
The theory of gamma ring has been introduced by Nobusawa in 1964 as a generalization of rings. In this
work, we generalized the notion of source of semi-primeness for gamma rings and investigated its basic
algebraic properties. We also defined SSMS -strongly reduced Γ-ring, SSMS -domain, SSMS -division ring and
examined the relationship between these structures. We determined all possible characteristic values of a
SSMS -domain and proved every finite SSMS -domain Γ-ring M is a SSMS -division Γ-ring.

References

  • Aydın N., Demir C., Camcı D.K., The source of semiprimeness of rings, Communications of the Korean Mathematical Society, 33(4), 1083-1096, 2018.
  • Barnes W., On the Γ -rings of Nobusawa, Pacific Journal of Mathematics, 18(3), 411-422, 1966.
  • Coppage W.E., Luh J., Radicals of gamma rings, Journal of the Mathematical Society of Japan, 23(1), 40-52, 1971.
  • Kandamar H., The k-derivation of a Gamma-ring, Turkish Journal of Mathematics, 23(3), 221-229, 2000.
  • Kyuno S., On the radicals of Γ-rings, Osaka Journal of Mathematics, 12(3), 639-645, 1975.
  • Kyuno S., On prime gamma rings, Pacific Journal of Mathematics, 75(1), 185-190, 1978.
  • Kyuno S., Gamma Rings, Hadronic Press, Inc., 1991.
  • Kyuno S., A gamma ring with minimum conditions, Tsukuba Journal of Mathematics, 5(1), 47-65, 1981.
  • Luh J., On the theory of simple Γ-rings, The Michigan Mathematical Journal, 16(1), 65-75, 1969.
  • McCoy N.H., The Theory of Rings, MacMillan, 1968.
  • Nobusawa N., On a generalization of the ring theory, Osaka Journal of Mathematics, 1(1), 81-89, 1964.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Okan Arslan 0000-0002-1006-066X

Nurcan Düzkaya 0000-0003-0733-3572

Publication Date July 31, 2023
Published in Issue Year 2023

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.