Vol. 16, No. 1, 1966

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ISSN: 0030-8730
A description of Multi(A1,,An) by generators and relations

Thomas William Hungerford

Vol. 16 (1966), No. 1, 61–76
Abstract

If R is a ring (with unit) and AR,R1AR2,,RAR,Rn1An are R-(bi)modules, then MultiR,n(A1,,An) is defined to be the i-th left derived functor of the multiple tensor product A1 An(= R); i.e., Hi(K1 Kn), where each Kr is a projective resolution of Ar.

The purpose of this paper is to give a description of MultiR,n(A1,,An) in terms of generators and relations, analogous to that given by MacLane in the case n = 2 [and Multi = ToriR(A1,A2)].

Mathematical Subject Classification
Primary: 16.90
Secondary: 18.20
Milestones
Received: 2 July 1964
Published: 1 January 1966
Authors
Thomas William Hungerford