# ring isomorphism

## ring isomorphism

[′riŋ ‚ī·sō′mȯr‚fiz·əm]
(mathematics)
An isomorphism between rings.
References in periodicals archive ?
Since all of the noncommutative symmetric functions in this section commute and satisfy the same defining relations as their commutative counterparts, there is a ring isomorphism
If V=eA then f eAe[right arrow][E.sub.A](eA) is a ring isomorphism. Thus in particular [E.sub.A]([A.sub.A])[approximately equal to]A[approximately equal to][E.sub.A]([sub.A]A).
is a ring isomorphism onto a subring of [Cart.sub.p]R ([14; IV, 4]).
Suppose B [[subset].bar] A and S [[subset].bar] R are ring extensions with ring isomorphism [PSI] : A [??] R restricting to a ring isomorphism [eta] : B [??] S.
Moreover, if [phi] is a bijection, then [phi] is called a neutrosophic ring isomorphism and we write [R.sub.1](I) [congruent to] [R.sub.2](I).
mapping as R([j.sub.L]), is a ring isomorphism such that R([j.sub.L]) = i x [[phi].sub.L], for the identical embedding i: R x L [right arrow] RL.
(1) There exist a ring isomorphism [PHI] : W([K.sub.1]) [right arrow] W([K.sub.2]) and a group isomorphism [PSI] : [W.sub.q]([K.sub.1]) [right arrow] [W.sub.q]([K.sub.2]) such that [PSI](b.q) = [PHI](b).[PSI](q) for all b [member of] W([K.sub.1]) and for all q [member of] [W.sub.q]([K.sub.1]).
It follows that {[[bar.x].sup.l][[bar.y].sup.m]|0 [??] l [??] n - 1, 0 [??] m [??] 2n - 2} is a Z-basis of Z[x,y]/I Consequently, [bar.[??]] is a Z-module isomorphism, and so it is a ring isomorphism.
Since the ring isomorphism [Z.sub.n] [congruent to] [Z.sub.p] x [Z.sub.q], the projectors [mu], [eta] from Y to U = [Z.sub.p] and V = [Z.sub.q] satisfy the hypothesis in Proposition 4.1.
Under the ring isomorphism that fixes the elements in [mathematical expression not reproducible] and [mathematical expression not reproducible] is isomorphic to the ring [mathematical expression not reproducible], where [u.sup.2] = 0.
Then (f, g) is called soft neutrosophic ring isomorphism.
the upper horizontal map is strict, and an isomorphism, corresponding to the ring isomorphism [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with (x, y) sent to (x'y, y) in k[x', y].
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