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In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M, either or . A module is called a serial module if it is a direct sum of uniserial modules. A ring R is called a right uniserial ring if it is uniserial as a right module over itself, and likewise called a right serial ring if it is a right serial module over itself. Left uniserial and left serial rings are defined in an analogous way, and are in general distinct from their right counterparts.

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rdfs:label	Serial module (en)
rdfs:comment	In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M, either or . A module is called a serial module if it is a direct sum of uniserial modules. A ring R is called a right uniserial ring if it is uniserial as a right module over itself, and likewise called a right serial ring if it is a right serial module over itself. Left uniserial and left serial rings are defined in an analogous way, and are in general distinct from their right counterparts. (en)
dcterms:subject	Module theory Ring theory
Wikipage page ID	31157948 (xsd:integer)
Wikipage revision ID	1061077759 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime power Endomorphism ring Epimorphism Module (mathematics) Monomorphism Principal ideal ring Prime ring David Eisenbud Alfred Goldie Module theory Paul Cohn Permutation Ring isomorphism Valuation ring Injective module Jacobson's conjecture Jacobson radical Quotient ring Ring theory Matrix (mathematics) Maximal submodule Normal subgroup Subring Krull-Schmidt theorem Gottfried Köthe Progenerator Linear isomorphism Commutative ring Composition series Tadashi Nakayama (mathematician) Matrix ring Maximal ideal Total order Domain (ring theory) Irving Kaplansky Local ring Duality (mathematics) Finite field Direct sum of modules Finitely presented module Quiver (mathematics) Ring (mathematics) Group (mathematics) Prime number Abstract algebra Characteristic (algebra) Sylow subgroup Hereditary ring Division ring Artinian ring Group ring Idempotent element (ring theory) Inclusion (set theory) Integer Catenary ring Semiperfect ring Semisimple ring Image (mathematics) Quasi-Frobenius ring Nakayama algebra Uniform module Semisimple module Noetherian Simple module Morita equivalent Upper triangular matrix Ring with unity Submodule Semilocal ring Superfluous submodule Essential submodule Unital module Cyclic submodule dbr:Local_module
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=PswhrD_wUIkC
sameAs	Serial module Serial module Serial module
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Redirect
has abstract	In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M, either or . A module is called a serial module if it is a direct sum of uniserial modules. A ring R is called a right uniserial ring if it is uniserial as a right module over itself, and likewise called a right serial ring if it is a right serial module over itself. Left uniserial and left serial rings are defined in an analogous way, and are in general distinct from their right counterparts. An easy motivating example is the quotient ring for any integer . This ring is always serial, and is uniserial when n is a prime power. The term uniserial has been used differently from the above definition: for clarification . A partial alphabetical list of important contributors to the theory of serial rings includes the mathematicians Keizo Asano, I. S. Cohen, P.M. Cohn, Yu. Drozd, D. Eisenbud, A. Facchini, A.W. Goldie, Phillip Griffith, I. Kaplansky, V.V Kirichenko, G. Köthe, H. Kuppisch, I. Murase, T. Nakayama, P. Příhoda, G. Puninski, and R. Warfield. References for each author can be found in and. Following the common ring theoretic convention, if a left/right dependent condition is given without mention of a side (for example, uniserial, serial, Artinian, Noetherian) then it is assumed the condition holds on both the left and right. Unless otherwise specified, each ring in this article is a ring with unity, and each module is unital. (en)
prov:wasDerivedFrom	wikipedia-en:Serial_module?oldid=1061077759&ns=0
page length (characters) of wiki page	16281 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Serial_module
is Link from a Wikipage to another Wikipage of	Principal ideal ring Valuation ring Descendant tree (group theory) Artinian ring Quasi-Frobenius ring Nakayama algebra Chain module Chain ring Serial ring

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