A class of rings between Armendariz and Central Armendariz rings

Subject Areas : Ring and Module Theory

Sh. Sahebi ¹ , S. Razaghi ²

1 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Department of mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2020-08-23 Accepted : 2020-11-03 Published : 2020-12-01

Keywords: Armendariz rings, idempotent element, abelian rings,

Abstract :

The purpose of this paper is to introduce a proper class of rings between Armendariz and Central Armendariz rings. In this direction, we define the concept of Idempotent Armendariz rings.We consider the closure of the $Id$-Armendariz rings with respect to various extensions includingdirect product, matrices rings, corner rings, polynomial rings and etc.

References:

[1] N. Agayev, G. Güngöroglu, A. Harmanci, S. Halicioglu, Central Armendariz rings, Bull. Malaysian. Math. Sci. Soc. 34 (1) (2011), 137-145.

[2] S. A. Amitsur, A note on extensions of Baer and P. P. -rings, Canad. J. Math. 8 (1956), 355-361.

[3] D. D. Anderson, V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra. 26 (7) (1998), 2265-2272.

[4] F. W. Anderson, K. R. Fuller, Rings and Catagories of Modules, Second Edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.

[5] C. Huh, Y. Lee, A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra. 30 (2) (2002), 751-761.

[6] Y. C. Jeon, H. K. Kim, Y. Lee, J. S. Yoon, On weak Armendariz ring, J. Pure Appl. Algebra. 146 (1) (2000), 35-44.

[7] N. K. Kim, Y. Lee, Armendariz rings and reduced rings, J. Algebra. 223 (2) (2000), 477-488.

[8] N. K. Kim, Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra. 185 (2003), 207-223.

[9] Z. Liu, R. Zhao, On weak Armendariz rings, Comm. Algebra. 34 (7) (2006), 2607-2616.

[10] M. B. Rege, S. Chhawchharia, Armendariz rings, Proc. Japan. Acad. Ser. A. Math. Sci. 73 (1997), 14-17.