The idea of intutionistic L-fuzzy subring
was introduced by K.
By imposing the vanishing condition mD on both sides of (0.1), we also obtain an isomorphism between the canonical ring [mathematical expression not reproducible] of [S.sub.[GAMMA]] and the following subring
of [[direct sum].sub.m][M.sub.3m]([GAMMA]):
Let D be a division ring and let R be the following subring
of [M.sub.3] (D) :
Caption: Figure 2: One-third subring
where a, c, e, g, 2b, 2d, 2f, 2h [member of] Z with [bar.2b] = [bar.2d] and [bar.2f] = [bar.2h], denoted by [bar.H](Q[[square root of (2)]]), is a subring
of H(Q[[square root of (2)]]).
(1) [LAMBDA] a set of indices, A a solid subring
of the ring [K.sup.[LAMBDA]] (that is to say, for any [mathematical expression not reproducible] (i.e., for any [lambda], [absolute value of ([s.sub.[lambda]])] [less than or equal to] [r.sub.[lambda]]), then [([s.sub.[lambda]]).sub.[lambda]] [member of] A), and [I.sub.A] a solid ideal of A;
Then the ring [mathematical expression not reproducible] is a commutative subring
of [mathematical expression not reproducible].
The homology and cohomology of the affine Grassmannian thus acquire an algebra structure; it follows from Bott's work  that [H.sub.*](Gr) and [H.sup.*](Gr) can be identified with a subring
[[LAMBDA].sub.(n)] and a quotient [[LAMBDA].sup.(n)] of the ring [LAMBDA] of symmetric functions.
I [subset] E is called an algebraic ideal of E if
Let [R.sub.c] [less than or equal to] End A be the subring
of R generated by the commutator actions: