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Rees factor
Let be an ideal of a semigroup . Define a congruence by iff or .
Then the Rees factor of by is the quotient . As a matter of notation, the congruence is normally suppressed, and the quotient is simply written .
Note that a Rees factor always has a zero element. Intuitively, the quotient identifies all element in and the resulting element is a zero element.
Related:
Ideal3
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
20M12 Ideal theory20M10 General structure theory
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