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Author | Title | Accn# | Year | Item Type | Claims |
| 1 |
Kaya, R |
Rings and Geometry |
I04785 |
1985 |
eBook |
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| 2 |
Plaumann, P |
Geometry ??? von Staudt???s Point of View |
I04380 |
1981 |
eBook |
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| 3 |
Barlotti, A |
Generators and Relations in Groups and Geometries |
I02261 |
1991 |
eBook |
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1.
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| Title | Rings and Geometry |
| Author(s) | Kaya, R;Plaumann, P;Strambach, K |
| Publication | Dordrecht, Springer Netherlands, 1985. |
| Description | XII, 568 p : online resource |
| Abstract Note | When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de?? veloped branch of mathematics has been dealt with in a variety of mono?? graphs, so that - in spite of its technical complexity - it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes- which right now has reached a peak once more - , the numerous other applications of ring theory in geometry have not been assembled in a textbook and are scattered in many papers throughout the literature, which makes it hard for them to emerge from the shadow of the brilliant theory of algebraic geometry. It is the aim of these proceedings to give a unifying presentation of those geometrical applications of ring theo~y outside of algebraic geometry, and to show that they offer a considerable wealth of beauti?? ful ideas, too. Furthermore it becomes apparent that there are natural connections to many branches of modern mathematics, e. g. to the theory of (algebraic) groups and of Jordan algebras, and to combinatorics. To make these remarks more precise, we will now give a description of the contents. In the first chapter, an approach towards a theory of non-commutative algebraic geometry is attempted from two different points of view |
| ISBN,Price | 9789400954601 |
| Keyword(s) | 1. ALGEBRA
2. EBOOK
3. EBOOK - SPRINGER
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| Item Type | eBook |
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Circulation Data
| Accession# | |
Call# | Status | Issued To | Return Due On | Physical Location |
| I04785 |
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On Shelf |
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3.
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| Title | Generators and Relations in Groups and Geometries |
| Author(s) | Barlotti, A;Ellers, E.W;Plaumann, P;Strambach, K |
| Publication | Dordrecht, Springer Netherlands, 1991. |
| Description | XV, 447 p : online resource |
| Abstract Note | Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char?? acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance |
| ISBN,Price | 9789401133821 |
| Keyword(s) | 1. ALGEBRA
2. DIFFERENTIAL GEOMETRY
3. EBOOK
4. EBOOK - SPRINGER
5. Field theory (Physics)
6. Field Theory and Polynomials
7. GROUP THEORY
8. Group Theory and Generalizations
9. Linear and Multilinear Algebras, Matrix Theory
10. MATRIX THEORY
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| Item Type | eBook |
Multi-Media Links
Please Click here for eBook
Circulation Data
| Accession# | |
Call# | Status | Issued To | Return Due On | Physical Location |
| I02261 |
|
|
On Shelf |
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