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REFLEXIVE PROPERTY ON IDEMPOTENTS
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 Title & Authors
REFLEXIVE PROPERTY ON IDEMPOTENTS
Kwak, Tai Keun; Lee, Yang;
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 Abstract
The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization. It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.
 Keywords
reflexive property;reflexive-idempotents-property (RIP);polynomial ring;Dorroh extension;minimal RIP ring;
 Language
English
 Cited by
1.
CORRIGENDUM TO "REFLEXIVE PROPERTY ON IDEMPOTENTS" [BULL. KOREAN MATH. SOC. 50 (2013), NO. 6, 1957-1972],;;

대한수학회보, 2016. vol.53. 6, pp.1913-1915 crossref(new window)
1.
Reflexivity with maximal ideal axes, Communications in Algebra, 2017, 45, 10, 4348  crossref(new windwow)
2.
CORRIGENDUM TO "REFLEXIVE PROPERTY ON IDEMPOTENTS" [BULL. KOREAN MATH. SOC. 50 (2013), NO. 6, 1957-1972], Bulletin of the Korean Mathematical Society, 2016, 53, 6, 1913  crossref(new windwow)
 References
1.
R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), no. 8, 3128-3140. crossref(new window)

2.
H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368. crossref(new window)

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

4.
P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), no. 6, 641-648. crossref(new window)

5.
J. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (1932), no. 2, 85-88. crossref(new window)

6.
K. E. Eldridge, Orders for finite noncommutative rings with unity, Amer. Math. Monthly 75 (1968), no. 5, 512-514. crossref(new window)

7.
S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186-199. crossref(new window)

8.
N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352-355.

9.
J. Y. Kim, Certain rings whose simple singular modules are GP-injective, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 7, 125-128. crossref(new window)

10.
J. Y. Kim and J. U. Baik, On idempotent reflexive rings, Kyungpook Math. J. 46 (2006), no. 4, 597-601.

11.
N. K. Kim, Y. Lee, and Y. Seo, Structure of idempotents in rings without identity, (submitted).

12.
T. K. Kwak and Y. Lee, Reflexive property of rings, Comm. Algebra, 40 (2012), no. 4, 1576-1594. crossref(new window)

13.
T. K. Kwak, Y. Lee, and S. J. Yun, The Armendariz property on ideals, J. Algebra 354 (2012), 121-135. crossref(new window)

14.
J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham, 1966.

15.
T. K. Lee and T. L. Wong, On Armendariz Rings, Houston J. Math. 29 (2003), no. 3, 583-593.

16.
T. K. Lee and Y. Q. Zhou, Armendariz and reduced rings, Comm. Algebra 32 (2004), no. 6, 2287-2299. crossref(new window)

17.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. crossref(new window)

18.
G. Mason, Reflexive ideals, Comm. Algebra 9 (1981), no. 17, 1709-1724. crossref(new window)

19.
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., 1987.

20.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. crossref(new window)

21.
J. C. Shepherdson, Inverses and zero-divisors in matrix ring, Proc. London Math. Soc. (3) 1 (1951), 71-85.

22.
L. Xu and W. Xue, Structure of minimal non-commutative zero-insertive rings, Math. J. Okayama Univ. 40 (1998), 69-76.