On the global dimension of fibre products.

In this paper we will sharpen Wiseman's upper bound on the global dimension of a fibre product [Theorem 2] and use our bound to compute the global dimension of some examples. Our upper bound is used to prove a new change of rings theorem [Corollary 4]. Lower bounds on the global dimension of a fibre product seem more difficult; we obtain a result [Proposition 12] which allows us to compute lower bounds in some special cases.

[1]  J. Kuzmanovich,et al.  On the global dimension of a ring modulo its nilpotent radical , 1988 .

[2]  J. Kuzmanovich,et al.  Matrix subrings having finite global dimension , 1987 .

[3]  J. T. Stafford.  Global dimension of semiprime noetherian rings , 1987 .

[4]  P. Vámos,et al.  Injective Modules over Pullbacks , 1985 .

[5]  A. N. Wiseman.  Projective modules over pullback rings , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  J. Robson.  Some constructions of rings of finite global dimension , 1985, Glasgow Mathematical Journal.

[7]  L. Small.  Rings satisfying a polynomial identity , 1980 .

[8]  J. E. Carrig.  The homological dimensions of symmetric algebras , 1978 .

[9]  B. Greenberg.  Coherence in Cartesian squares , 1978 .

[10]  Wolmer V. Vasconcelos,et al.  The rings of dimension two , 1976 .

[11]  B. Greenberg.  Global dimension of cartesian squares , 1974 .

[12]  Vasanti A. Jategaonkar.  Global dimension of tiled orders over commutative noetherian domains , 1974 .

[13]  J. Roos,et al.  Explicit formulae for the global homological dimensions of trivial extensions of rings , 1973 .

[14]  J. Robson,et al.  Idealizers and hereditary noetherian prime rings , 1972 .

[15]  K. Fields.  On the global dimension of residue rings. , 1970 .

[16]  Richard B. Tarsy.  Global dimension of orders , 1970 .

[17]  K. Fields.  Examples of orders over discrete valuation rings , 1969 .

[18]  Irving Kaplansky,et al.  Fields and rings , 1969 .

[19]  C. U. Jensen.  On Homological Dimensions of Rings with Countably Generated Ideals. , 1966 .