Titlebook: Algebra II Ring Theory; Vol. 2: Ring Theory Carl Faith Book 1976 Springer-Verlag Berlin Heidelberg 1976 Ring.algebra

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https://doi.org/10.1007/978-3-658-28729-0ulo annihilator 19.14A. Over a right Artinian ring, any QI right module is finendo and conversely 19.16. Thus, every faithful quasinjective over a right Artinian ring is injective 19.15, a result which holds for finitely generated faithful modules over commutative rings 19.17.

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Gefahren im technischen Umfeld,. Σ. means that every (injective) right .-module is a direct sum of cyclic modules. (Note that one applies these designations to . as an object of RINGS rather than as an object of mod-.; strictly speaking, it is mod-. (not . that is (injective) Σ-finitely generated when we say that . is.)

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Schutzaspekte beim Betrieb eines Rechners,The UD theorem 18.18 is extended in this chapter to infinite Azumaya diagrams (AD’s) in an . category 21.6. Other results are (1) the .-lemma 21.1; (2) the cancellation theorem 21.2; (3) .-adically complete rings 21.7–8; (4) summands of AD’s of injective modules are again AD’s 21.15 (cf. 21.14).

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Datenschutz und Datensicherheit,In this chapter we introduce Morita duality. Roughly speaking, these theorems are dual to the Morita theorems on category equivalence (Chapter 12).

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Algebra II Ring Theory978-3-642-65321-6Series ISSN 0072-7830 Series E-ISSN 2196-9701

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0072-7830 Overview: 978-3-642-65323-0978-3-642-65321-6Series ISSN 0072-7830 Series E-ISSN 2196-9701