Abstract
There is an invariant of rings called the global dimension. Semisimple rings are precisely those rings with global dimension zero. Thus the material in Chapters 1 and 2 can be considered the zero’th step in the theory of global dimension. Kaplansky, based upon an observation of Schanuel, was the first to set down the dimension theory of rings in an elementary way, without using the powerful machinery of homological algebra. This section is based on his Queen Mary College notes.
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© 1993 Springer Science+Business Media New York
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Farb, B., Dennis, R.K. (1993). The Global Dimension of a Ring. In: Noncommutative Algebra. Graduate Texts in Mathematics, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0889-1_8
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DOI: https://doi.org/10.1007/978-1-4612-0889-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6936-6
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