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1991•Journal of Information and Optimization SciencesRequires access

Generalized Affine Planes

Franco Eugeni, Antonio Maturo

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Abstract

In this paper a class of generalized affine planes over the ring of residues modu lus n is investigated. If n is a prime number then a generalized affine plane come down to an affine Galois plane, but, if n is not a prime number then the properties of a generalized affine plane are very different from Galois plane’s. For instance, it can occur that there are many lines containing two distinct points and moreover that the numbers of points of two lines are different. In this paper we prove some theorems that characterize the generalized affine planes.

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What this paper is about

In this paper a class of generalized affine planes over the ring of residues modu lus n is investigated. If n is a prime number then a generalized affine plane come down to an affine Galois plane, but, if n is not a prime number then the properties of a generalized affine plane are very different from Galois plane’s. For instance, it can occur that there are many lines containing two distinct points and moreover that the numbers of points of two lines are different. In this paper we prove some theorems that characterize the generalized affine planes.

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Available abstract

In this paper a class of generalized affine planes over the ring of residues modu lus n is investigated. If n is a prime number then a generalized affine plane come down to an affine Galois plane, but, if n is not a prime number then the properties of a generalized affine plane are very different from Galois plane’s. For instance, it can occur that there are many lines containing two distinct points and moreover that the numbers of points of two lines are different. In this paper we prove some theorems that characterize the generalized affine planes.

Key concepts: Affine transformation, Mathematics, Computer science, Combinatorics, Pure mathematics

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