The primitive $n^ {th}$ roots of unity form basis over $\mathbb {Q . . . We fix the primitive roots of unity of order $7,11,13$, and denote them by $$ \tag {*} \zeta_7,\zeta_ {11},\zeta_ {13}\ $$ Now we want to take each primitive root of prime order from above to some power, then multiply them When the number of primes is small, or at least fixed, the notations are simpler
Primitive and modular ideals of $C^ {\ast}$-algebras So $\ker\pi$ is primitive but not modular To find a modular ideal that is not primitive, we need to start with a unital C $^*$ -algebra (so the quotient will be unital) and consider a non-irreducible representation
Are all natural numbers (except 1 and 2) part of at least one primitive . . . Hence, all odd numbers are included in at least one primitive triplet Except 1, because I'm not allowing 0 to be a term in a triplet I can't think of any primitive triplets that have an even number as the hypotenuse, but I haven't been able to prove that none exist
What is a free group element that is not primitive? A primitive element of a free group is an element of some basis of the free group I have seen some recent papers on algorithmic problems concerning primitive elements of free groups, for example,
Primitive integer triangles - Mathematics Stack Exchange An integer sided triangle $ (a,b,c)$ is called primitive if $\gcd (a,b,c)=1$ How many primitive integer-sided triangles exist with a perimeter not exceeding $10 000 000$? I am trying to solve this on Euler project I am wondering what is the best way to go to find the valid triples for constructing a triangle
Basis of primitive nth Roots in a Cyclotomic Extension? Another method to show the "only if " direction is to use the fact that the trace of $\zeta_n$ is equal to zero if n is not square free, while by definition, the trace of $\zeta_n$ in this case is exactly the same as the sum of all the primitive n-th roots of unity, so we have a linearly dependent relation over $\mathbb {Q}$ for all the primitive n-th roots, so they could not form a basis, see