# ON EXCHANGE IDEALS

• CHEN, HUANYIN
• Published : 2005.05.01
• 47 13

#### 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 $QM_2$(I). Also we observe that every exchange ideal can be characterized by exchange elements.

#### Keywords

exchange ideal;matrix ring;extension

#### References

1. P. Ara, Extensions of exchange rings, J. Algebra, 197 (1997), 409-423 https://doi.org/10.1006/jabr.1997.7116
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 https://doi.org/10.1007/BF02780325
3. P. Ara, G. K. Pedersen, and F. Perera, An infinite analogue of rings with stable range one, J. Algebra, 230 (2000), 608-655 https://doi.org/10.1006/jabr.2000.8330
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 https://doi.org/10.1023/A:1009927211591
6. H. Chen, Units, idempotents and stable range conditions, Comm. Algebra 29 (2001), 703-717 https://doi.org/10.1081/AGB-100001535
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 https://doi.org/10.1016/S0022-4049(02)00299-2
9. W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278 https://doi.org/10.2307/1998510
10. W. K. Nicholson, On exchange rings, Comm. Algebra 25 (1977), 1917-1918 https://doi.org/10.1080/00927879708825962
11. E. Pardo, Comparability, separativity, and exchange rings, Comm. Algebra 24 (1996), 2915-2929 https://doi.org/10.1080/00927879608825721
12. F. Perera, Lifting units modulo exchange ideals and C'-algebras with real rank zero, J. Reine. Angew. Math. 522 (2000), 51-62