The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual...

In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated lcm-lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose lcm-lattice is P , and we give a characterization of all such coordinatizations. We prove that all relations in the lattice L(n) of all finite atom...

0. Introduction. The literature on algebraic semigroups contains publications concerning two distinct types of semigroup extensions. Ideal extensions of semigroups were introduced by Clifford in [1] whereas Rédei [9] introduced Schreier extensions of monoids (a monoid is a semigroup containing an identity element). Let A and 5 be two disjoint semigroups and let 5" contain a zero element o. A se...

We )nd that adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information. The optimal ratio r of inhibitory to excitatory inputs for decoding the input information from an observation of the e,erent interspike intervals is calculated. Surprisingly, the Fisher information could be zero for certain values of the ratio, seemingly impl...

We prove the following result: Theorem. Every algebraic distributive lattice D with at most א1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the א1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. F...

We construct an Identity-Based Key Encapsulation Mechanism (IBKEM) in a generic “leveled” multilinear map setting and prove its security under multilinear decisional Diffie-Hellmanin assumption in the selective-ID model. Then, we make our IB-KEM translated to the GGH framework, which defined an “approximate” version of a multilinear group family from ideal lattices, and modify our proof of secu...

We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen [8]. In particular, we give a characterization of ideal well-rounded lattices in the plane and show that a positive proportion of real and imaginary quadratic number fields contains ideals giving rise to well-rounded lattices.

Given a finite dimensional Lie algebra $L$ let $I$ be the augmentation ideal in universal enveloping $U(L)$. We study conditions on under which $Ext$-groups $Ext (k,k)$ for trivial $L$-module $k$ are same when computed category of all $U(L)$-modules or $I$-torsion $U(L)$-modules. also prove that Rees $\oplus _{n\geq 0}I^n$ is Noetherian if and only nilpotent. An application to cohomology equiva...

Let A be an associative algebra over a field F of characteristic zero and let L Lie F. If acts on by derivations, then such action determines its universal enveloping U(L) in this case we refer to as with derivations or L-algebra. Here give characterization the ideal differential identities finite dimensional L-algebras corresponding sequence codimensions ${c_{n}^{L}} (A)$ , n ≥ 1, is polynomia...

We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke L-functions. In forthcoming work of the second author, these estimates will be used to establish explicit bounds on the least norm of a prime ideal in a congruence class group and improve upon existing explicit bounds for the least norm of a prime ideal...