Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Coalgebraic Coalgebras

D. E. Radford
Proceedings of the American Mathematical Society
Vol. 45, No. 1 (Jul., 1974), pp. 11-18
DOI: 10.2307/2040598
Stable URL: http://www.jstor.org/stable/2040598
Page Count: 8
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Coalgebraic Coalgebras
Preview not available

Abstract

We investigate coalgebras C over a field k such that the dual algebra C* is an algebraic algebra (C is called coalgebraic). The study reduces to the cosemisimple and connected cases. If C is cosemisimple and coalgebraic, then C* is of bounded degree. If C is connected, then C is coalgebraic if, and only if, every coideal is the intersection of cofinite coideals. Our main result is that if C is a coalgebra over an infinite field k and the Jacobson radical $\operatorname{Rad} C^\ast$ is nil, there is an n such that an = 0 all $a \in \operatorname{Rad} C^\ast$. By the Nagata-Higman theorem, $\operatorname{Rad} C^\ast$ is nilpotent if nil is characteristic 0.

Page Thumbnails

  • Thumbnail: Page 
11
    11
  • Thumbnail: Page 
12
    12
  • Thumbnail: Page 
13
    13
  • Thumbnail: Page 
14
    14
  • Thumbnail: Page 
15
    15
  • Thumbnail: Page 
16
    16
  • Thumbnail: Page 
17
    17
  • Thumbnail: Page 
18
    18