we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

New family of flat potential (Darboux–Egoroff) metrics on the Hurwitz spaces and corresponding Frobenius structures are found. We consider a Hurwitz space as a real manifold. Therefore the number of coordinates is twice as big as the number of coordinates used in the construction of Frobenius structure on Hurwitz spaces found by B. Dubrovin more than 10 years ago. The branch points of a ramifie...

Abstract A numerical semigroup is a sub-monoid of the natural numbers under addition that has finite complement. The size its complement called genus and largest number in Frobenius number. We consider set semigroups with fixed f analyse their genus. find asymptotic distribution this show it product Gaussian power series. almost all have close to $$\frac{3f}{4}$$ <mml:math xmlns:mml="http://www...

Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. The Frobenius number of this N -tuple is defined to be the largest positive integer that has no representation as PN i=1 aixi where x1, ..., xN are nonnegative integers. More generally, the s-Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques...

In this paper, we characterize those numerical semigroups containing 〈n1, n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators.

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.