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Addendum to ‘Embedding GCD Domains in Bezout Domains’
Author(s) -
Shamash Josephine,
Smith Stuart T.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.2.209
Subject(s) - addendum , citation , embedding , mathematics , algebra over a field , computer science , library science , philosophy , artificial intelligence , pure mathematics , linguistics
It has come to our attention that the main theorem in our paper [3] had appeared previously in the literature, in an article by P. M. Cohn [1]. Although the results are essentially the same, our proof is completely different from his and may therefore be of interest. We have developed the definition of content of a polynomial in a certain extension of a GCD domain; Prof. Cohn generalized the notion of GCD domain to that of a Schreier domain and worked with the latter. In fact the Schreier property developed in his paper proves itself to be useful in the study of models of open induction, a weak fragment of Peano arithmetic. It is shown in [4] that the Schreier property is preserved by all of the constructions described in [2] except for D and H. Thus most of the pathological models of open induction constructed in [2] can be taken to be Schreier domains.