The total quotient ring Q ( A \ times B ) of a product ring is the product of total quotient rings Q ( A ) \ times Q ( B ).
22.
This implies that " p " is an irreducible polynomial, and thus that the quotient ring K [ X ] / \ langle p \ rangle is a field.
23.
The latter can be easily done by taking, for all nonzero elements of the quotient ring, a sequence starting from a point beyond the last zero element of the sequence.
24.
The starting point is a Noetherian, regular, " n "-dimensional ring and a full flag of prime ideals such that their corresponding quotient ring is regular.
25.
Since S in the construction contains no zero divisors, the natural map R \ to Q ( R ) is injective, so the total quotient ring is an extension of R.
26.
Meaning the " n "-fold tensor product of itself, is represented as the quotient ring of a polynomial algebra by a homogeneous ideal " I ".
27.
18 ) " The product is natural because the quotient ring R X S / R is isomorphic to S and similarly R X S / S is isomorphic to R . " Huh?
28.
I think that mainly intuition regarding the " concepts " must be given ( like ideals, quotient rings etc . . . ) . talk ) 13 : 13, 22 December 2008 ( UTC)
29.
Quotient rings are distinct from the so-called'quotient field', or field of fractions, of an integral domain as well as from the more general'rings of quotients'obtained by localization.
30.
With the development of quotient rings of polynomial rings, the concept behind an imaginary number became more substantial, but then one also finds other imaginary numbers such as the j of tessarines which has a square of.
