Localization at prime ideals in bounded rings

Document Type : Research Paper


Hacettepe University‎, ‎Department of Mathematics‎, ‎06800 Beytepe‎, ‎Ankara‎, ‎Turkey.


In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.


Main Subjects

A. Braun and C.R. Hajarnavis, Generator ideals in Noetherian PI rings, J. Algebra 247 (2002) 134--152.
H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, NJ, 1956.
A.W. Chatters and S.M. Ginn, Localisation in hereditary rings, J. Algebra 22 (1972), no. 1, 82--88.
A.W. Chatters and C.R. Hajarnavis, Rings with Chain Conditions, Research Notes in Math. 44, Pitman Advanced Pub. Program, Boston, 1980.
D. Eisenbud and J.C. Robson, Hereditary Noetherian prime rings, J. Algebra 16 (1970), no. 1, 86--104.
A.W. Goldie, Localisation in non-commutative Noetherian rings, J. Algebra 5 (1967), no. 1, 89--105.
K.R. Goodearl and R.B. Warfield, An introduction to Noncommutative Noetherian Rings, Cambridge Univ. Press, New York, 2004.
C.R. Hajarnavis, One sided invertibility and localisation, Glasg. Math. J. 34 (1992), no. 3, 333--339.
C.R. Hajarnavis and T.H. Lenagan, Localisation in Asano orders, J. Algebra 21 (1972) 441--449.
O. Ore, Theory of noncommutative polynomials, Ann. of Math. 34 (1933) 480--508.
P.F. Smith, Localization and the AR property, Proc. Lond. Math. Soc. 22 (1971), no. 3, 39--68.