ON II-ARMENDARIZ RINGS

Title & Authors
ON II-ARMENDARIZ RINGS
Huh, Chan; Lee, Chang-Ik; Park, Kwang-Sug; Ryu, Sung-Ju;

Abstract
We in this note introduce a concept, so called $\small{{\pi}-Armendariz}$ ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of $\small{{\pi}-Armendariz}$ rings, constructing typical examples. We next extend the class of $\small{{\pi}-Armendariz}$ rings, through various ring extensions.
Keywords
$\small{{\pi}-Armendariz}$ ring;2-primal ring;Armendariz ring;nilpotent element;
Language
English
Cited by
1.
On Rings Having McCoy-Like Conditions, Communications in Algebra, 2012, 40, 4, 1195
2.
Nil-Armendariz rings relative to a monoid, Arabian Journal of Mathematics, 2013, 2, 1, 81
3.
ON Π-NEAR-ARMENDARIZ RINGS, Asian-European Journal of Mathematics, 2009, 02, 01, 77
4.
On nilpotent elements of ore extensions, Asian-European Journal of Mathematics, 2017, 10, 03, 1750043
5.
On linearly weak Armendariz rings, Journal of Pure and Applied Algebra, 2015, 219, 4, 1122
6.
On Skew Triangular Matrix Rings, Algebra Colloquium, 2015, 22, 02, 271
7.
π-Armendariz rings relative to a monoid, Frontiers of Mathematics in China, 2016, 11, 4, 1017
References
1.
D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2272

2.
E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473

3.
G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and as- sociated radicals, Ring theory (Granville, OH, 1992), 102-129, World Sci. Publ., River Edge, NJ, 1993

4.
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Regularity conditions and the simplicity of prime factor rings, J. Pure Appl. Algebra 115 (1997), no. 3, 213-230

5.
Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), no. 1, 45-52

6.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761

7.
N. K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), no. 2, 477-488

8.
T.-K. Lee and T.-L. Wong, On Armendariz rings, Houston J. Math. 29 (2003), no. 3, 583-593

9.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123

10.
G. Marks, A taxonomy of 2-primal rings, J. Algebra 266 (2003), no. 2, 494-520

11.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17

12.
G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43-60