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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Three sets of conditions on rings


Author: Abraham A. Klein
Journal: Proc. Amer. Math. Soc. 25 (1970), 393-398
MSC: Primary 16.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0263869-0
MathSciNet review: 0263869
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Abstract: We define a set of conditions $ {\mathfrak{L}_m}$ on a ring $ R$ using the notion of $ R$-dependence of elements. We prove that $ {\mathfrak{L}_1},{\mathfrak{L}_2}, \cdots $ is a strictly decreasing sequence of conditions. Two other sequences of conditions are considered and we prove that they are also strictly decreasing and we obtain their relation to $ {\mathfrak{L}_m}$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0263869-0
Keywords: Left and right $ R$-dependent, $ m$-fir, $ m$-term algorithm, formal series, special series
Article copyright: © Copyright 1970 American Mathematical Society

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