In object-oriented databases, schema design or evolution BKKK87] should beneet as much as possible from automatic tools. In this paper, we focus on the automatic insertion of classes into inheritance hierarchies, while preserving a \maximal factorizing" of class properties. We describe an incremental algorithm which factors properties, approaches the overloading problem, and can be used to buil...

let $cr_{n}(f)$ denote the algebra of $n times n$ circulant matrices over the field $f$. in this paper, we study the unit group of $cr_{n}(f_{p^m})$, where $f_{p^m}$ denotes the galois field of order $p^{m}$, $p$ prime.

Much work has gone into matrix representations of Galois groups, but there is a whole new class of naturally occurring representations that have as yet gone almost unnoticed. In fact, it is well-known in various areas of mathematics that the main sources of totally disconnected groups are matrix groups over local fields AND automorphism groups of locally finite trees [12]. It is perhaps surpris...

Computing the Galois group of the splitting field of a given polynomial with integer coefficients is a classical problem in modern algebra. A theorem of Van der Waerden [Wae] asserts that almost all (monic) polynomials in Z[x] have associated Galois group Sn, the symmetric group on n letters. Thus, cases where the associated Galois group is different from Sn are rare. Nevertheless, examples of ...

A field K admits proper projective extensions, i.e. Galois extensions where the Galois group is a nontrivial projective group, unless K is separably closed or K is a pythagorean formally real field without cyclic extensions of odd degree. As a consequence, it turns out that almost all absolute Galois groups decompose as proper semidirect products. We show that each local field has a unique maxi...

In this paper we deene a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the deenition of Galois connection and some of its properties; next we deene Lagois connection, establish some of its properties, and compare these with properties of Galois connections; and then we (further) dev...

We introduce new constructions of systematic authentication codes over finite fields and Galois rings. One code is built over finite fields using resilient functions and it provides optimal impersonation and substitution probabilities. Other two proposed codes are defined over Galois rings, one is based on resilient maps and it attains optimal probabilities as well, while the other uses maps wh...

We study the question of surjectivity Galois correspondence from subHopf algebras to subfields given by Fundamental Theorem Theory for abelian Hopf structures on a extension fields with group G', finite p-group. Applying connection between regular subgroups holomorph p-group (G, +) and associative, commutative nilpotent algebra A Caranti, et. al., we show that if gives rise H-Hopf structure L/K...