Construct · 1 fields · 1 citations

cancel: a standalone construct

One name. One construct. A landmark on the map.

● anchor · a standalone construct Nearest construct by meaning·not indexed
cancel1 CONSTRUCTCancellation lawCANCELLATIVE LAW

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Abstract algebra

Common factors can be struck from both sides

In algebra, to cancel is to apply the cancellation law: in a structure where ab = ac forces b = c (left cancellation) or ba = ca forces b = c (right cancellation), the common factor may be struck from both sides without inverting it. A semigroup in which this always holds is called cancellative, a property strictly weaker than having inverses yet strong enough to embed many such structures in groups. Clifford and Preston's The algebraic theory of semigroups develops cancellative semigroups as a core class. The referent is a structural property of a binary operation, not a mark on paper or a note in a score.[1]

Unit
Whether a common factor may be removed from both sides of an equation
Recovery means
Not applicable
Measured by
Established by proving the implication ab=ac → b=c (and its right-handed form) holds for all elements

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Nearby constructs

accidental2 fields · 3 citationsjingle · one word, two constructs

References

  1. Clifford, A. H., & Preston, G. B. (1961). The algebraic theory of semigroups (Vol. 1). American Mathematical Society. ISBN 9780821802717

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