Internal Duality for Resolutions of Rings
نویسندگان
چکیده
Section 0. Introduction The following example provided the motivation for this paper. Let F8 be the field with 8 elements, and let F8 be its group of units which acts on F8 via left multiplication. The cohomology ring H(F8 ×7 F8; F2) ∼= F2[x1, x2, x3] is of much interest to topologists ([A], [CS], [M]). It is a straight forward exercise to construct minimal sets of homogeneous generators and relations for this ring: there are 13 generators and 54 relations. The surprising fact is that the minimal relations exhibit a certain internal duality:
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