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On Sasiada's Ring
Author(s) -
Leavitt W. G.,
Tangeman R. L.
Publication year - 1970
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/s2-2.1.32-s
Subject(s) - modulo , lemma (botany) , corollary , mathematics , monomial , formal power series , pure mathematics , ideal (ethics) , combinatorics , remainder , discrete mathematics , power series , arithmetic , philosophy , mathematical analysis , epistemology , ecology , poaceae , biology
It has been pointed out to us by P. M. Cohn that in the proof of Lemma 2 the tacit assumption is made that J is a closed ideal. It is assumed, namely, that since x 3 commutes modulo J with all monomials it will therefore commute modulo J with all formal power series. Since J is not closed this need not be true in general. Thus Lemma 2 should be deleted, and hence also Propositions 1 and 2 and Corollary 1. The results of the remainder of the paper are independent and are believed to be correct. Also note that in the proof of Lemma 3 the contents of the first bracket should be x − yx 2 y .