# Cyclic semirings with idempotent noncommutative addition

## Related Articles

- A tracial Nullstellensatz. Klep, Igor; Špenko, Špela // Bulletin of the London Mathematical Society;Oct2014, Vol. 46 Issue 5, p1091
The main result of this note is a tracial Nullstellensatz for free noncommutative polynomials evaluated at tuples of matrices of all sizes: Suppose $f_1,\ldots ,f_r,f$ are free polynomials, and $\mathrm {tr} (f)$ vanishes whenever all $\mathrm {tr} (f_j)$ vanish. Then either $1$ or $f$ is a...

- On the second rational K-group of an elliptic curve over global fields of positive characteristic. Kondo, Satoshi; Yasuda, Seidai // Proceedings of the London Mathematical Society;Jun2011, Vol. 102 Issue 6, p1053
Let E be an elliptic curve over a global field of positive characteristic. Let r be the order of zero at s=0 of the Hasseâ€“Weil L-function with bad factors removed. The Parshin conjecture on the vanishing of higher rational K-theory of projective smooth schemes over finite fields implies...

- ON THE AVERAGE OF THE LEAST PRIMITIVE ROOT MODULO p. ELLIOTT, P. D. T. A.; MURATA, LEO // Journal of the London Mathematical Society;12/01/1997, Vol. 56 Issue 3, p435
In this paper we study the value distribution of the least primitive root to a prime modulus, as the modulus varies. For each odd prime number p, we shall denote by g(p) and G(p) the least primitive root and the least prime primitive root (mod p), respectively. Numerical examples show that, in...

- HAMMOCKS AND THE NAZAROVA-ROITER ALGORITHM. LIN, YANAN // Journal of the London Mathematical Society;04/01/1998, Vol. 57 Issue 2, p309
Hammocks have been considered by Brenner [1], who gave a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck [11] gave a combinatorial definition of left hammocks which generalised the concept of...

- Classification of Permutation Trinomials and Quadrinomials Over Prime Fields. Rybalkin, M. // Journal of Mathematical Sciences;Aug2014, Vol. 200 Issue 6, p734
We present a method for enumerating the permutation trinomials and quadrinomials using various symmetries and algebraic properties to reduce the search space. Applying this method, we enumerated all permutation trinomials and quadrinomials for the prime finite fields with orders up to 3000 and...

- Complexity of computation in finite fields. Gashkov, S.; Sergeev, I. // Journal of Mathematical Sciences;Jun2013, Vol. 191 Issue 5, p661
We give a review of some works on the complexity of implementation of arithmetic operations in finite fields by Boolean circuits.

- On the existence for some special primitive elements in finite fields. Liao, Qunying; Li, Jiyou; Pu, Keli // Chinese Annals of Mathematics;Mar2016, Vol. 37 Issue 2, p259
Let F be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive element $$\alpha \in {F_{{q^n}}}$$ such that Î± + Î± is also primitive or Î± + Î± is primitive and Î± is a normal element...

- On Derivations of Prime Î“-Semirings. Javed, M. A.; Aslam, M.; Hussain, M. // Southeast Asian Bulletin of Mathematics;2013, Vol. 37 Issue 6, p859
In this paper, we introduce the notion of derivations of prime Î“-semirings and extend a few results of E.C. Posner in the frame work of derivations of prime Î“-semirings.

- Commuting Regular G-Semiring. Krishnamoorthy, S.; Doss, R. Arul // International Journal of Computational & Mathematical Sciences;Autumn2010, Vol. 4 Issue 8, p376
We introduce the notion of commuting regular G- semiring and discuss some properties of commuting regular G- semiring. We also obtain a necessary and sufficient condition for G-semiring to possess commuting regularity.