Total algebra
id:
total-algebra-297-11219545
title:
Total algebra
text:
In abstract algebra, the total algebra of a monoid is a generalization of the monoid ring that allows for infinite sums of elements of a ring. Suppose that S is a monoid with the property that, for all s ∈ S , there exist only finitely many ordered pairs ∈ S × S for which t u = s . Let R be a ring. Then the total algebra of S over R is the set R S of all functions α : S → R with the addition law given by the (pointwise) operation: and with the multiplication law given by: The sum on the right-ha
brand slug:
wiki
category slug:
encyclopedia
description:
Generalization of monoid ring
original url:
https://en.wikipedia.org/wiki/Total_algebra
date created:
date modified:
2024-01-13T14:59:27Z
main entity:
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image:
fields total:
13
integrity:
14