Undergraduate Algebra by Matej Brešar

Author:Matej Brešar
Language: eng
Format: epub
ISBN: 9783030140533
Publisher: Springer International Publishing

Comment. This result is called the Chinese Remainder Theorem. It was known, in some form, to Chinese mathematicians almost two millennia ago.

4.103.

Although named and denoted in the same way, commutators in rings are defined differently as in groups. A commutator in a ring R is an element of the form with . We write this element as [x, y]. Let denote the ideal of R generated by all commutators [x, y] in R. Prove that is commutative and that is contained in every ideal I of R with the property that R/I is commutative. Describe in the case where R is the ring of all upper triangular real matrices.

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