Download E-books Semidistributive Modules and Rings (Mathematics and Its Applications) PDF

A module M is named distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is termed uniserial if all its submodules are similar with appreciate to inclusion, i.e., the lattice Lat(M) is a series. Any direct sum of distributive (resp. uniserial) modules is named a semidistributive (resp. serial) module. the category of distributive (resp. semidistributive) modules safely cont.ains the category ofall uniserial (resp. serial) modules. specifically, all easy (resp. semisimple) modules are distributive (resp. semidistributive). All strongly usual earrings (for instance, all issue jewelry of direct items of department earrings and all commutative average earrings) are distributive; all valuation earrings in department earrings and all commutative Dedekind jewelry (e.g., earrings of critical algebraic numbers or commutative central perfect earrings) are distributive. A module is termed a Bezout module or a in the community cyclic module ifevery finitely generated submodule is cyclic. If all maximal correct beliefs of a hoop A are beliefs (e.g., if A is commutative), then all Bezout A-modules are distributive.

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