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Embedding Right Chain Rings in Chain Rings

Published online by Cambridge University Press:  20 November 2018

H. H. Brungs  and
G. Törner
H. H. Brungs
Affiliation:
University of A Iberta, Edmonton, Alberta
G. Törner
Affiliation:
University of A Iberta, Edmonton, Alberta
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The following problem was the starting point for this investigation: Can every desarguesian affine Hjelmslev plane be embedded into a desarguesian projective Hjelmslev plane [8]? An affine Hjelmslev plane is called desarguesian if it can be coordinatized by a right chain ring R with a maximal ideal J(R) consisting of two-sided zero divisors. A projective Hjemslev plane is called desarguesian if the coordinate ring is in addition a left chain ring, i.e. a chain ring. This leads to the algebraic version of the above problem, namely the embedding of right chain rings into suitable chain rings. We can prove the following result.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 5 , 01 October 1978 , pp. 1079 - 1086
Copyright
Copyright © Canadian Mathematical Society 1978

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