… Divisors arise also in categories of modules generated by spherical modules - modules … In
the last chapter a divisor is defined in the category of modules of finite injective dimension but …

… In Chapters 23 and 24, we study Morita's duality theory for a category mod-A of right A-modules.
Dual to the idea of equivalence is that of a duality CD between categories: namely, TS≈ …

… In Chapter 3 we develop basic module theory. This chapter culminates in the structure
theorem for finitely generated modules over a PID. (We then specialize to obtain the basic …

… We introduce and study zero-divisor graphs in categories of left modules over a ring R, ie
R-MOD. The vertices of Γ(R-MOD) consist of all nonzero morphisms in R-MOD which are not …

… theory, as shown in torsion theory and localization. On the other hand, the application of
category theory … method in ring theory itself. To pursue this idea, we must define new concepts in …

… and modules, and then we develop the structure theory for modules over various kinds of ring.
… The necessary category theory is dealt with in the companion volume [BK: CM], both in the …

… module theory and, for M = Ä, we obtain well-known results for the entire module category
over … (1) An idempotent e ER which is not a (right) unit is a right zero divisor: For some a E Rwe …

… and 3 we introduce modules and their homomorphisms. In Section 4 we see that these form
various natural and important categories, and we begin our study of categories of modules. …

… In general, we identify cyclic modules over various semiring categories with different flavors
of algebraic theories, all of which can be folded … 1 Z=n, where each prime divisor of n is in S . …

… theory KV C for the nice categories parametrized by rings. When applied to projective modules
we recover the Karoubi-Villamayor Af-theory … set of central nonzero divisors of the ring R, …