A finite ring R and a weight w on R satisfy the Extension Property if every R linear w -isometry between two R -linear codes in R extends to a monomial transformation of R n that preserves w . MacWilliams proved that finite fields with the Hamming weight satisfy the Extension Property. It is known that finite Frobenius rings with either the Hamming weight or the homogeneous weight satisfy the E...

Let R be a (nonzero commutative unital) ring. If I and J are ideals of R such that R/I ⊕R/J is a cyclic R-module, then I + J = R. The rings R such that R/I ⊕R/J is a cyclic R-module for all distinct nonzero proper ideals I and J of R are the following three types of principal ideal rings: fields, rings isomorphic to K ×L for the fields K and L, and special principal ideal rings (R,M) such thatM...

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...

Let K be a number field and ` a positive integer. The main theorem of [3] gives an upper bound for the order of the `-torsion subgroup in the ideal class group ClK of K under the Generalized Riemann Hypothesis, which can be made unconditional in certain special cases (e.g. when K/Q is a quadratic extension and ` = 3.) The main idea is to show that there are many ideal classes which are not `-to...

using a bessel generalized translation, we obtain an analog of titchmarsh's theorem for the bessel transform for functions satisfying the lipschitz condition in the space $mathrm{l}_{p,alpha}(mathbb{r}_{+})$, where $alpha>-frac{1}{2}$ and $1

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

We give a new characterisation of elliptic curves Shimura type in terms commuting families Frobenius lifts and also strengthen an old principal ideal theorem for ray class fields. These two results combined yield the existence global minimal models type, generalising result Gross. Along way we prove handful small but regarding with complex multiplication.