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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Semidistributive Modules and Rings

Semidistributive Modules and Rings

Tuganbaev, A. a.

Paperback

Series: Mathematics and Its Applications, Book 449

Algebra

ISBN10: 940106136X
ISBN13: 9789401061360
Publisher: Springer Nature
Published: Oct 15 2012
Pages: 357
Weight: 1.15
Height: 0.77 Width: 6.14 Depth: 9.21
Language: English
A module M is called 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 called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive.

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