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with the replacement of "field" and "vector space" with "commutative ring" and "module".

Unital zero algebras allow the unification of the theory of submodules of a given module and the theory of ideals of a unital algebra. Indeed, the submodules of a module correspond exactly to the ideals of that are contained in .

For example, the theory of Gröbner bases was introduced by Bruno Buchberger for

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