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Results tagged with ac.commutative-algebra
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user 30395
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Formalization of the independance of products in a (commutative) semigroup
1/ It is well known that associativity implies that the result of the product of an ordered finite set of elements in a semigroup does not depend of the order of composition of the partial products.
H …
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Examples of semirings where the additive neutral element is not absorbing for multiplication
In the case of a non unital ring, the additive 0 must be absorbing for the multiplication because we have a⋅0 = a⋅(a − a) = a⋅a − a⋅a = 0 and similarly on the other side.
In the case of a unital semi …
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Is every commutative group structure underlying at least one (unitary, commutative) ring str...
From the theorem of classification of finitely generated abelian groups, we can see that every finitely generated commutative group can be considered as the additive structure underlying (at least) on …
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Free commutative magma over a set
BOURBAKI, inside his book on ALGEBRA defines and provides explicit constructions concerning the concepts of free magma, free monoid (and implicitly free semi-group) and free group, and as well free co …
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