ON EXCHANGE IDEALS

Title & Authors
ON EXCHANGE IDEALS
CHEN, HUANYIN;

Abstract
In this paper, we investigate exchange ideals and get some new characterization of exchange rings. It is shown that an ideal I of a ring R is an exchange ideal if and only if so is $\small{QM_2}$(I). Also we observe that every exchange ideal can be characterized by exchange elements.
Keywords
exchange ideal;matrix ring;extension;
Language
English
Cited by
References
1.
P. Ara, Extensions of exchange rings, J. Algebra, 197 (1997), 409-423

2.
P. Ara, K. R. Goodearl, K. C. O'Meara, and E. Pardo, Separative cancellation for projective modules over exchange rings, Israel J. Math. 105 (1998), 105-137

3.
P. Ara, G. K. Pedersen, and F. Perera, An infinite analogue of rings with stable range one, J. Algebra, 230 (2000), 608-655

4.
V. P. Camillo and H. P. Yu, Exchange rings, units and idempotents, Comm. Algebra 22 (1994), 4737-4749

5.
H. Chen, Exchange rings with artinian primitive factors, Algebra Represent. Theory, 2 (1999), 201-207

6.
H. Chen, Units, idempotents and stable range conditions, Comm. Algebra 29 (2001), 703-717

7.
H. Chen, Exchange rings with stable range conditions in: recent research on pure and applied algebra, O. Pordavi(Ed.), Nova Science Publishers, Inc., New York, 2003, 47-58

8.
C. Y. Hong, N. K. Kim, and Nam Y. Lee, Exchange rings and their extensions, J. Pure Appl. Algebra 179 (2003), 117-126

9.
W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278

10.
W. K. Nicholson, On exchange rings, Comm. Algebra 25 (1977), 1917-1918

11.
E. Pardo, Comparability, separativity, and exchange rings, Comm. Algebra 24 (1996), 2915-2929

12.
F. Perera, Lifting units modulo exchange ideals and C'-algebras with real rank zero, J. Reine. Angew. Math. 522 (2000), 51-62