Abstract
In commutative algebra, a local ring is defined to be a (nonzero) ring which has a unique maximal ideal. This definition generalizes readily to arbitrary rings: a (nonzero) ring A is said to be local if A has a unique maximal left ideal. This definition turns out to be left-right symmetric, and is equivalent to the condition that A/rad A be a division ring.
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© 1995 Springer Science+Business Media New York
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Lam, T.Y. (1995). Local Rings, Semilocal Rings, and Idempotents. In: Exercises in Classical Ring Theory. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3987-9_7
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DOI: https://doi.org/10.1007/978-1-4757-3987-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3989-3
Online ISBN: 978-1-4757-3987-9
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