in which H is a residually finite dimensional Hopf algebra, H[degrees] is its finite dual Hopf algebra, which is dense in H*, and L is a dense subring
Then NQS is called a neutrosophic quadruple subring
of NQR if (NQS, +,.
1) [LAMBDA] a set of indices, A a solid subring
of the ring [K.
Then the ring [mathematical expression not reproducible] is a commutative subring
of [mathematical expression not reproducible].
I [subset] E is called an algebraic ideal of E if
c] [less than or equal to] End A be the subring
of R generated by the commutator actions:
1) For n = 2k [greater than or equal to] 4 and positive integer i, j satisfied k [greater than or equal to] i [greater than or equal to] 1, k [greater than or equal to] j [greater than or equal to] i and i [not equal to] 1 when j = k, any subring
Lemma 3: Let B be a subring
of A with 1 [member of] B such that B satisfies A.
An intuitionistic fuzzy subset A of R is said to be an intuitionistic fuzzy subring
of R (IFSR) if it satisfies the following axioms:
o](M), the ring of continuous real-valued functions on M, [Mathematical Expression Omitted], the subring
of bounded continuous functions, and [C.
We claim that Z is a Nash manifold, and that I is a real ideal, so that, by the real Nullstellensatz, the ring D = A[z]/I is a subring
of the ring N (Z) of Nash functions of Z.
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