Semidistributive Modules and Rings
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...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Radicals, local and semisimple modules
- 1.1 Maximal submodules and the Jacobson radical
- 1.2 Local and uniserial modules
- 1.3 Semisimple and Artinian modules
- 1.4 The prime radical
- 2 Projective and injective modules
- 2.1 Free and projective modules
- 2.2 Injective modules
- 2.3 Injective hull
- 3 Bezout and regular modules
- 3.1 Regular modules
- 3.2 Unit-regular rings
- 3.3 Semilocal rings and distributivity
- 3.4 Strongly regular rings
- 3.5 Bezout rings
- 4 Continuous and finite-dimensional modules
- 4.1 Closed submodules
- 4.2 Continuous modules
- 4.3 Finile-dimensional modules
- 4.4 Nonsingular ?-injective modules
- 5 Rings of quotients
- 5.1 Ore sets
- 5.2 Denominator sets and localizable rings
- 5.3 Maximal rings of quotients
- 6 Flat modules and semiperfect rings
- 6.1 Characterizations of flat modules
- 6.2 Submodules of flat modules
- 6.3 Semiperfect and perfect rings
- 7 Semihereditary and invariant rings
- 12.3 Subgroups, submonoids, and annihilators
- 12.4 Regular group rings
- 12.5 Cancellative monoids
- 12.6 Semilattices and regular monoids
- 7.1 Coherent and reduced rings
- 7.2 Invariant rings
- 7.3 Rings with integrally closed factor rings
- 8 Endomorphism rings
- 8.1 Modules over endomorphism rings and quasi injective modules
- 8.2 Nilpotent endomorphisms
- 8.3 Strongly indecomposable modules
- 9 Distributive rings with maximum conditions
- 9.1 Arithmetics of ideals
- 9.2 Noel.herian rings
- 9.3 Classical rings of quotients of distributive rings
- 9.4 Rings algebraic over their centre
- 10 Self-injective and skew-injective rings
- 10.1 Quasi-frobenius rings and direct sums of injective modules
- 10.2 Cyclic ?-injective modules
- 10.3 Integrally closed Noetherian rings
- 10.4 Cyclic skew-injective modules
- 10.5 Countably injective rings
- 11 Semidistributive and serial rings
- 11.1 Semidistributive modules
- 11.2 Semidistributive rings
- 11.3 Serial modules and rings
- 12 Monoidrings and related topics
- 12.1 Series and polynomial rings
- 12.2 Quaternion algebras