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sanctifier
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Notations:
M denotes an abelian group under addtion
R denotes a commutative ring with identity
ann(?): Let M be an R-module and r∈R v∈M, then ann(v)={r∈R | rv=0}
Terms:
R-module: a module whose base ring is R
torsion element: A nonzero element v∈M for which rv=0 for some nonzero r∈R
torsion module: all elements of the module are torsion elements
integral domain: a commutative ring R with identity with the property that for r,s∈R, rs≠0 if r≠0 and s≠0
Question:
Find a torsion module M for which ann(M)={0}.
I wonder whether the base ring R of such M can only be an integral domain.
M denotes an abelian group under addtion
R denotes a commutative ring with identity
ann(?): Let M be an R-module and r∈R v∈M, then ann(v)={r∈R | rv=0}
Terms:
R-module: a module whose base ring is R
torsion element: A nonzero element v∈M for which rv=0 for some nonzero r∈R
torsion module: all elements of the module are torsion elements
integral domain: a commutative ring R with identity with the property that for r,s∈R, rs≠0 if r≠0 and s≠0
Question:
Find a torsion module M for which ann(M)={0}.
I wonder whether the base ring R of such M can only be an integral domain.