Meaning of quotient ring | Babel Free

Definitions

For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R.

Equivalents

Examples

“The third section covers a construct similar to the ring⟳ S°R — the maximal quotient ring⟳, which exists for any ring⟳. (When R is nonsingular, the maximal quotient ring⟳ is exactly S°R.) Finally, Section D provides an answer⟳ to the question⟳ of which right and left nonsingular rings have⟳ coinciding maximal right and left quotient rings.”

“On the other hand if already every element of R is either invertible or a zerodivisor, then R is its own⟳ classical quotient ring⟳.”

“2. An ideal P of the ring⟳ R is prime if and only if the quotient ring⟳ R/P is a domain.”

CEFR level