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Gluing Two Affine Spaces
"... A construction is described in [2]... In this paper we will examine a special case of that construction, namely the gluing of two affine spaces. ..."
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A construction is described in [2]... In this paper we will examine a special case of that construction, namely the gluing of two affine spaces.
THE CANCELLATION PROBLEM FOR AFFINE SPACES
, 2008
"... The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that: Let k be an algebraically closed field of characteristic zero and let n, m ∈ N. If R[Y1,...,Ym] ∼ =k k[X1,..., Xn+m] as kalgebras, where ..."
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The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that: Let k be an algebraically closed field of characteristic zero and let n, m ∈ N. If R[Y1,...,Ym] ∼ =k k[X1,..., Xn+m] as kalgebras, where
Transformations in Affine Spaces 1
"... Summary. Two classes of bijections of its point universe are correlated with every affine structure. The first class consists of the transformations, called formal isometries, which map every segment onto congruent segment, the second class consists of the automorphisms of such a structure. Each of ..."
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of these two classes of bijections forms a group for a given affine structure, if it satisfies a very weak axiom system (models of these axioms are called congruence spaces); formal isometries form a normal subgroup in the group of automorphism. In particular ordered affine spaces and affine spaces
An Affine Space over a Module
"... Abstract. In the paper basic notions of an affine space over a linear space, usually called an affine space over a field, have been made generalizations in an affine space over a module. Some properties of the affine mapping in an affine space over a module are also investigated. Isomorphism of affi ..."
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Abstract. In the paper basic notions of an affine space over a linear space, usually called an affine space over a field, have been made generalizations in an affine space over a module. Some properties of the affine mapping in an affine space over a module are also investigated. Isomorphism
Transformations in Affine Spaces 1
"... Summary. Two classes of bijections of its point universe are correlated with every affine structure. The first class consists of the transformations, called formal isometries, which map every segment onto congruent segment, the second class consists of the automorphisms of such a structure. Each of ..."
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of these two classes of bijections forms a group for a given affine structure, if it satisfies a very weak axiom system (models of these axioms are called congruence spaces); formal isometries form a normal subgroup in the group of automorphism. In particular ordered affine spaces and affine spaces
SemiAffine Space 1
"... Summary. A brief survey on semiaffine geometry, which results from the classical Pappian and Desarguesian affine (dimension free) geometry by weakening the so called trapezium axiom. With the help of the relation of parallelogram in every semiaffine space we define the operation of ”addition ” of ..."
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Summary. A brief survey on semiaffine geometry, which results from the classical Pappian and Desarguesian affine (dimension free) geometry by weakening the so called trapezium axiom. With the help of the relation of parallelogram in every semiaffine space we define the operation of ”addition
Fanoian, Pappian and Desarguesian Affine Spaces
"... this paper. Let O 1 be an ordered affine space. One can check that (O 1 ) is affine spacelike and non trivial. Let O 1 be an ordered affine plane. Note that (O 1 ) is 2dimensional. The following propositions are true: (2) ..."
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this paper. Let O 1 be an ordered affine space. One can check that (O 1 ) is affine spacelike and non trivial. Let O 1 be an ordered affine plane. Note that (O 1 ) is 2dimensional. The following propositions are true: (2)
Affine Spaces within Projective Spaces
"... We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not ass ..."
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We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do
Fundamental Types of Metric Affine Spaces
"... Summary. We distinguish in the class of metric affine spaces some fundamental types of them. First we can assume the underlying affine space to satisfy classical affine configurational axiom; thus we come to Pappian, Desarguesian, Moufangian, and translation spaces. Next we distinguish the spaces sa ..."
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Summary. We distinguish in the class of metric affine spaces some fundamental types of them. First we can assume the underlying affine space to satisfy classical affine configurational axiom; thus we come to Pappian, Desarguesian, Moufangian, and translation spaces. Next we distinguish the spaces
Analytical Ordered Affine Spaces 1
"... Summary. In the article with a given arbitrary real linear space we correlate the (ordered) affine space defined in terms of a directed parallelity of segments. The abstract contains a construction of the ordered affine structure associated with a vector space; this is a structure of the type which ..."
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Summary. In the article with a given arbitrary real linear space we correlate the (ordered) affine space defined in terms of a directed parallelity of segments. The abstract contains a construction of the ordered affine structure associated with a vector space; this is a structure of the type which
Results 1  10
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283,807