On Ring Structures Under Strong Cup Products

Abstract

Can we construct a strong s-stage cohomology ring on inverse systems? The following statements show the answer to this question: After defining a strong cup product, we construct a ring structure with right identity under strong cup product and obtain a strong cup product preserving homomorphism induced by a rigid system map on the level of strong s-stage cochain groups. On the other hand, we show that the coboundary formula for strong s-stage cochains does not hold.

Key Words:

• Rigid system map
• Strong cup product
• Strong (s-stage) homology

2000 Mathematics Subject Classification:

• Primary 16W80, 16W50
• Secondary 55N45

ACKNOWLEDGMENTS

The author is grateful to the referees for pointing out errors in the original manuscript and for offering other suggestions that improved the quality of the article.

This article was supported by research funds of Chonbuk National University in 2009.

Notes

Communicated by J. Zhang.