Search Results for ""

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

A group in which any decreasing chain of distinct subgroups terminates after a finite number.

A module that fulfils the descending chain condition with respect to inclusion, i.e., if every decreasing sequence of submodules eventually become constant.

A ring is called left (respectively right) Artinian if it does not contain an infinite descending chain of left (resp. right) ideals. In this case the ring in question is ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

A series is called artistic if every three consecutive terms have a common three-way ratio P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)). A series is ...

The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M ...

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...