Class field theory describes the abelian extensions of a number field using the arithmetic of that field. The Kronecker-Weber theorem states that all abelian extensions of the rationals are contained in cyclotomic fields. As we know, cyclotomic fields can be generated by special values of the exponential function e, and we call this the theory of complex multiplication for Gm. We would thus lik...

in vitro propagation of plant has played a very important role in rapidmultiplication of cultivars with desirable traits and production of healthy and disease-free plants. in the present investigation, the objectives were to optimize the micropropagation of rose hybrid ‘black baccarat’ cultivar. in proliferation step, the nodal segments (1.5 cm) was cultured on both liquid and solid media (ms, ...