Three sets of conditions on rings
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- by Abraham A. Klein
- Proc. Amer. Math. Soc. 25 (1970), 393-398
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263869-0
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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 ${\mathfrak {L}_m}$.References
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- Abraham A. Klein, Rings nonembeddable in fields with multiplicative semi-groups embeddable in groups, J. Algebra 7 (1967), 100–125. MR 230749, DOI 10.1016/0021-8693(67)90070-1
- Abraham A. Klein, Necessary conditions for embedding rings into fields, Trans. Amer. Math. Soc. 137 (1969), 141–151. MR 236212, DOI 10.1090/S0002-9947-1969-0236212-7
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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