some examples of nontrivial homotopy groups of modules

Clicks: 90
ID: 162943
2001
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #164 of 403 articles by views in structural engineering and mechanics

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 403 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Abstract
The concept of the homotopy theory of modules was discovered by Peter Hilton as a result of his trip in 1955 to Warsaw, Poland, to work with Karol Borsuk, and to Zurich, Switzerland, to work with Beno Eckmann. The idea was to produce an analog of homotopy theory in topology. Yet, unlike homotopy theory in topology, there are two homotopy theories of modules, the injective theory, π¯n(A,B), and the projective theory, π¯n(A,B). They are dual, but not isomorphic. In this paper, we deliver and carry out the precise calculation of the first known nontrivial examples of absolute homotopy groups of modules, namely, π¯n(ℚ/ℤ,ℚ/ℤ),  π¯n(ℤ,ℚ/ℤ), and π¯n(ℤ,ℤ), where ℚ/ℤ and ℤ are regarded as ℤCk-modules with trivial action. One interesting phenomenon of the results is the periodicity of these homotopy groups, just as for the Ext groups.
Reference Key
su2001internationalsome Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;C. Joanna Su
Journal structural engineering and mechanics
Year 2001
DOI
10.1155/S0161171201005373
URL
Keywords

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

No comments yet. Be the first to comment on this article.