Abstract
Bu makale, R halkasının birimleri ile sıfır bölücülerinin değişmeli olması hakkındadır. Bu halkalara tek-sıfır bölücü halkalar denir. Burada tek-sıfır bölücü halkalarının birçok karakterizasyonu, iyi bilinen halka sınıflarıyla karşılaştırılır.
References
- [1] Alwis T., 1994. “The ideal structure of Z ∗ Z”, Missouri J. Math. Sci, 6 , 116123. [2] Anderson DD., Bennis D., Fahid B., Shaiea A., “On n-trivial Extensions of Rings”, arXiv:1604.01486. [3] Calugareanu G., 2018 . “Rings whose units commute with nilpotent elements”, Mathematica., 60 (83), 1-8. [4]Chebotar M., Lee P.-H., Puczylowski E. R., 2009. “On prime rings with commuting nilpotent elements”, Bull. Korean Math. Soc. (9)137, 2899-2903. [5] Khurana D., Marks G. and Srivastava A. (2010). “On unit-central rings”, Advances in ring theory 205-212, Trends Math., Birkhauser-Springer Basel AG, Basel. [6] Lam T. Y., (1995). “Exercises in Classical Ring Theory”. Problem Books in Math., Springer Verlag , [7] Nicholson W. K., Springer H. J., 1976. “Commutativity of rings with abelian or solvable units”, Proc. Amer. Math. Soc., (1) 56 5962. [8] Mesyan Z., 2010. “The ideals of an ideal extension”, J. Algebra Appl., 3, 407431.
Abstract
This paper is about rings R for which units commute with zero divisors. These rings are called uni-zero divisor rings. It is deduced that uni-zero divisor ring is not abelian and also give several examples of some important classes of rings (a kind of integral matrices, matrix ring over any stably finite ring ) that are not uni-zero divisor ring. Here many characterizations of uni-zero divisor rings are compared with well-known classes of rings. Moreover, the uni-zero divisor rings property is studied under some algebraic constructions.
References
- [1] Alwis T., 1994. “The ideal structure of Z ∗ Z”, Missouri J. Math. Sci, 6 , 116123. [2] Anderson DD., Bennis D., Fahid B., Shaiea A., “On n-trivial Extensions of Rings”, arXiv:1604.01486. [3] Calugareanu G., 2018 . “Rings whose units commute with nilpotent elements”, Mathematica., 60 (83), 1-8. [4]Chebotar M., Lee P.-H., Puczylowski E. R., 2009. “On prime rings with commuting nilpotent elements”, Bull. Korean Math. Soc. (9)137, 2899-2903. [5] Khurana D., Marks G. and Srivastava A. (2010). “On unit-central rings”, Advances in ring theory 205-212, Trends Math., Birkhauser-Springer Basel AG, Basel. [6] Lam T. Y., (1995). “Exercises in Classical Ring Theory”. Problem Books in Math., Springer Verlag , [7] Nicholson W. K., Springer H. J., 1976. “Commutativity of rings with abelian or solvable units”, Proc. Amer. Math. Soc., (1) 56 5962. [8] Mesyan Z., 2010. “The ideals of an ideal extension”, J. Algebra Appl., 3, 407431.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | December 31, 2020 |
| Published in Issue | Year 2020 Volume: 13 Issue: 3 |