Vol. 15, No. 4, 1965

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Some remarks on the coefficients used in the theory of homology manifolds

Frank Albert Raymond

Vol. 15 (1965), No. 4, 1365–1376

In the theory of generalized n-manifolds (n-gms) or Čech cohomology manifolds (n-cms), as developed principally by Wilder, the ring of coefficients had been a field. Due to the influence of transformation groups interest was aroused for more general coefficient systems. However, it is usually simpler to deal algebraically with coefficients in a field. Thus it becomes desirable to have a theorem which implies the validity of a result for n-cms over principal ideal domains when it is known to be valid for fields. The main result of our paper is devoted to such a theorem.

Mathematical Subject Classification
Primary: 55.30
Secondary: 55.66
Received: 7 November 1963
Revised: 13 July 1964
Published: 1 December 1965
Frank Albert Raymond