We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an a...

An algorithm is given for determining all power integral bases in orders of totally real cyclic sextic number fields. The orders considered are in most cases the maximal orders of the fields. The corresponding index form equation is reduced to a relative Thue equation of degree 3 over the quadratic subfield and to some inhomogeneous Thue equations of degree 3 over the rationals. At the end of t...

Under Greenberg’s conjecture, we give an efficient method to compute the p-part of the ideal class group of certain real abelian fields by using cyclotomic units, Gauss sums and prime numbers. As numerical examples, we compute the p-part of the ideal class group of the maximal real subfield of Q( √ −f, ζpn+1) in the range 1 < f < 200 and 5 ≤ p < 100000. In order to explain our method, we show a...

Let (K,v) be a valued field, and μ an inductive valuation on K[x] extending v. Gμ the graded algebra of over K[x], κ maximal subfield subring formed by homogeneous elements degree zero. In this paper, we find algorithm to compute field residual polynomial operator Rμ:K[x]→κ[y], where y is another indeterminate, without any need perform computations in algebra. This leads OM factorization separa...

Received 16 March 2008; accepted 4 May 2008 Abstract: We classify the maximal irreducible periodic subgroups of PGL(q,F) , where F is a field of positive characteristic p transcendental over its prime subfield, q 6= p is prime, and F× has an element of order q . That is, we construct a list of irreducible subgroups G of GL(q,F) containing the centre F×1q of GL(q,F) , such that G/F×1q is a maxim...

BACKGROUND AND PURPOSE Automated subfield volumetry of hippocampus is desirable for use in temporal lobe epilepsy (TLE), but its utility has not been established. Automatic segmentation of hippocampal subfields (ASHS) and the new version of FreeSurfer software (ver.6.0) using high-resolution T2-weighted MR imaging are candidates for this volumetry. The aim of this study was to evaluate hippocam...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of family $[{2^{m}+1, 2u-1, 2^{m}-2u+3}]$ MDS for notation="LaTeX">$1 \leq u 2^{m-1}$ , which cyclic, reversible ...