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Then (RNQ(H), [symmetry]) is a hypergroup with identity element [bar.0] = (0, [p.summation over (i=1)] 0[T.sub.i], [R.summation over(j=1)] 0[I.sub.j], [r.summation over(k=1)] 0[F.sub.k]) if and only if (H, +) is a hypergroup with identity element 0.
and the connected component of the identity element equals the whole group.
To get a meaningful definition, we cannot let Magnus choose the identity element. The token starts at the identity element of G.
Similarly, n-ary semigroup (R, g) has an identity element 1 if
It is also easy to see that s * t [member of] H is the identity element of ([G.sub.H], [omicron]).
However our understanding is that monoids include an identity element and semigroups do not.
Since [a.sup.2][[omicron].sub.x] = ([R.sup.-1.sub.a][a.sup.2])([L.sup.-1.sub.a]x) = a([L.sup.-1.sub.a]x) = [L.sub.a][L.sup.-1.sub.a]x = x and similarly x [omicron] [a.sup.2] = x for all x [member of] B, [a.sup.2] is an identity element in B.
It follows that A is the identity element of this structure by symmetry.
Let U be the complexified universal enveloping algebra of the real Lie algebra g of G; which is canonically isomorphic onto the algebra of all distributions on G supported by {0} , where 0 is the identity element of G.
In some analyses, a salient identity element has been MHC's placement on the occupation-profession continuum (cf.
Part 2 contains chapters that address identity in earl y, middle, and late adolescence, as well as a further chapter of selected issues posing additional identity challenges for a substantial number of adolescents in the general population; all of these special challenges involve coming to terms with difference resulting from a nonchosen identity element. Part 3 contains chapters addressing identity development during the early, middle, and later years of adulthood.