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quotient ring
(redirected from Quotient algebra)

   Also found in: Wikipedia 0.01 sec.
quotient ring [′kwō·shənt ‚riŋ]
(mathematics)
A ringR/Iwhose elements are the cosetsrIof a given idealIin a given ringR, where the additive and multiplicative operations have the form:r1I+r2I≡ (r1+r2)Iandr1I·r2I≡ (r1·r2)I. Also known as factor ring; residue class ring.


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Therefore, up to this equivalence relation on the classes of formulas A', the quotient algebra rises to the so-called Rieger--Nishimura lattice R, which is a single-generated free Heyting algebra (see Figure 2).
A topological algebra A over C is a Gelfand-Mazur algebra if the quotient algebra A/M is topologically isomorphic to C for every M [member of] m(A).
 
 
 
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