Information om | Engelska ordet R-MODULES

Exempel på hur man kan använda R-MODULES i en mening

• Jacobson radical, consisting of those elements in a ring R that annihilate all simple right R-modules.
• thumbIn mathematics, more specifically ring theory, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules.
• Authors who do not require rings to be unital omit condition 4 in the definition above; they would call the structures defined above "unital left R-modules".
• This is then a left R-module, and the *-operation yields a faithful contravariant functor from right R-modules to left R-modules.
• Given a commutative ring R, an element x in R, and an R-module M, the multiplication by x yields a homomorphism of R-modules,.
• of (left) R-modules is pure exact if the sequence stays exact when tensored with any (right) R-module X.
• The depth of Q as an R-module is defined in that paper to be the least positive integer n such that Q⊗⋅⋅⋅⊗Q (n times Q, tensor product of R-modules, diagonal action of R from the right) has the same constituent indecomposable modules as Q ⊗⋅⋅⋅⊗ Q (n+1 times Q) (not counting multiplicities, an entirely similar definition for depth of Q as an H-module with closely related results).

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