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The Steenrod Algebra is a Prime Ring and the Krull Dimensions of the Steenrod Algebra

Stephens, Robert P.
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1309972869

Abstract Details

2011, Doctor of Philosophy, University of Toledo, Mathematics.
Kashkarev has shown that the mod 2 Steenrod algebra is a prime ring. For any odd prime p, we prove that the mod p Steenrod algebra is also a prime ring. In sequel, for any prime p, we show that the mod p Steenrod algebra (a local ring with nil maximal ideal) has infinite little Krull dimension. This contrasts sharply with the case of a commutative (or noetherian) local ring with nil maximal ideal which must have little Krull dimension equal to 0. Also, we show that the Steenrod algebra has no Krull dimension, classical Krull dimension, or Gabriel dimension.
Charles Odenthal, PhD (Committee Chair)
Paul Hewitt, PhD (Committee Member)
John Palmieri, PhD (Committee Member)
Martin Pettet, PhD (Committee Member)
76 p.
Mathematics
Steenrod algebra; prime ring; Krull dimension

Recommended Citations

Citations

  • Stephens, R. P. (2011). The Steenrod Algebra is a Prime Ring and the Krull Dimensions of the Steenrod Algebra [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1309972869

    APA Style (7th edition)

  • Stephens, Robert. The Steenrod Algebra is a Prime Ring and the Krull Dimensions of the Steenrod Algebra. 2011. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1309972869.

    MLA Style (8th edition)

  • Stephens, Robert. "The Steenrod Algebra is a Prime Ring and the Krull Dimensions of the Steenrod Algebra." Doctoral dissertation, University of Toledo, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1309972869

    Chicago Manual of Style (17th edition)

toledo1309972869
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© 2011, all rights reserved.
This open access ETD is published by University of Toledo and OhioLINK.
Release 3.2.12