zero module 예문

예문

1. A trivial algebra over a field is simultaneously a zero vector space considered algebra is simultaneously a zero module.
2. An indecomposable module is a non-zero module that cannot be written as a direct sum of two non-zero submodules.
3. If, for some, the th syzygy module is free, then, by taking a basis as a generating set, the next syzygy module ( and every subsequent one ) is the zero module.
4. Some authors work only over integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the ring contains zero divisors then the only module satisfying this condition is the zero module.
5. As the relations form a module, one may consider the relations between the relations; Hilbert's syzygy theorem asserts that, if one continues in this way, starting with a module over a polynomial ring in indeterminates over a field, one eventually finds a zero module of relations, after at most steps.