Serial module
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.
Arithmetical ringArtinian ringBalanced moduleChain moduleChain ringDecomposition of a moduleDescendant tree (group theory)Endomorphism ringGlossary of ring theoryHomogeneously serial moduleNakayama algebraPrimary decomposable ringPrincipal ideal ringPrüfer domainQuasi-Frobenius ringRing (mathematics)Semi-local ringSerial ringUniform moduleUniserial moduleUniserial ringValuation ring
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Serial module
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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In abstract algebra, a uniseri ...... ty, and each module is unital.
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In abstract algebra, a uniseri ...... from their right counterparts.
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Serial module
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