Manual Surface Topology (Mathematics and Its Applications (Ellis Horwood Ltd))

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Mailorder only - Alleen verzending mogelijk. Condition : very good. Ex-library With usual stamps and markings In poor condition suitable as a reading copy.

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With figures. Cover shows mild wear. ISBN: Hardcover, Previous owner's boookplate on fep and pocket glued to rear end page, small moisture stain at top edge of rear end page. Otherwise textblock is clean and tight.

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Lightly shelf worn binding, bumped corners. Light edge and spine wear to unclipped dust jacket, moderately rubbed covers, small moisture stain on top edge of back end flap. Clausen Books namus [Livres de Clausen Books]. Volume Re-bound by library. In fair condition suitable as a study copy.

Series: Lecture Notes in Mathematics, Minor wear. Older phraseology of older versions of Newton gives needless difficulties to the reader, but the judicious employment of new mdern ters enables the student to follow Newton's argument, but not lose the distinctive flavor of his thesis.

Classification of combinatorial surfaces (I) - Algebraic Topology - NJ Wildberger

Fine in Very Good dust jacket. Mossback Books namus [Livres de Mossback Books]. With usual stamps and markings In good all round condition. The topology of compact surfaces through the development of some simple ideas in plane geometry, an approach which allows a straight forward yet rigorous treatment of an area of mathematics that is particularly attractive both for the richness of its applications, and for the variety of its interactions with other branches of mathematics.

Laminate boards. Books by P. Firby 1.

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Books by C. Gardiner 1. Books published by Ellis Horwood Ltd 7. Stock no. Nearly fine condition. Among the four axioms above, the first two are elementary consequences of the definition, whereas the remaining two hinge on important facts in commutative algebra , the going-up theorem and Krull's principal ideal theorem. Similarly as for other algebraic structures, a ring homomorphism is thus a map that is compatible with the structure of the algebraic objects in question.

In such a situation S is also called an R -algebra, by understanding that s in S may be multiplied by some r of R , by setting. The kernel is an ideal of R , and the image is a subring of S. A ring homomorphism is called an isomorphism if it is bijective. An example of a ring isomorphism, known as the Chinese remainder theorem , is. Commutative rings, together with ring homomorphisms, form a category. By means of this map, an integer n can be regarded as an element of R.

For example, the binomial formula. Given two R -algebras S and T , their tensor product. In some cases, the tensor product can serve to find a T -algebra which relates to Z as S relates to R. For example,.

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An R -algebra S is called finitely generated as an algebra if there are finitely many elements s 1 , Equivalently, S is isomorphic to. A much stronger condition is that S is finitely generated as an R -module , which means that any s can be expressed as a R -linear combination of some finite set s 1 , A ring is called local if it has only a single maximal ideal, denoted by m.

For any not necessarily local ring R , the localization.

Surface Topology by P a Firby C F Gardiner - AbeBooks

This localization reflects the geometric properties of Spec R "around p ". Several notions and problems in commutative algebra can be reduced to the case when R is local, making local rings a particularly deeply studied class of rings. The residue field of R is defined as. Informally, the elements of m can be thought of as functions which vanish at the point p , whereas m 2 contains the ones which vanish with order at least 2. For any Noetherian local ring R , the inequality.

If equality holds true in this estimate, R is called a regular local ring. A Noetherian local ring is regular if and only if the ring which is the ring of functions on the tangent cone. Broadly speaking, regular local rings are somewhat similar to polynomial rings. Discrete valuation rings are equipped with a function which assign an integer to any element r. This number, called the valuation of r can be informally thought of as a zero or pole order of r.

Discrete valuation rings are precisely the one-dimensional regular local rings. For example, the ring of germs of holomorphic functions on a Riemann surface is a discrete valuation ring.

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By Krull's principal ideal theorem , a foundational result in the dimension theory of rings , the dimension of. A ring R is called a complete intersection ring if it can be presented in a way that attains this minimal bound. This notion is also mostly studied for local rings.

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Any regular local ring is a complete intersection ring, but not conversely. A ring R is a set-theoretic complete intersection if the reduced ring associated to R , i. As of , it is in general unknown, whether curves in three-dimensional space are set-theoretic complete intersections.

The depth of a local ring R is the number of elements in some or, as can be shown, any maximal regular sequence, i. A local ring in which equality takes place is called a Cohen—Macaulay ring. Local complete intersection rings, and a fortiori, regular local rings are Cohen—Macaulay, but not conversely.


Cohen—Macaulay combine desirable properties of regular rings such as the property of being universally catenary rings , which means that the co dimension of primes is well-behaved , but are also more robust under taking quotients than regular local rings. There are several ways to construct new rings out of given ones. The aim of such constructions is often to improve certain properties of the ring so as to make it more readily understandable. For example, an integral domain that is integrally closed in its field of fractions is called normal. This is a desirable property, for example any normal one-dimensional ring is necessarily regular.

Rendering [ clarification needed ] a ring normal is known as normalization.

If I is an ideal in a commutative ring R , the powers of I form topological neighborhoods of 0 which allow R to be viewed as a topological ring. This topology is called the I -adic topology. R can then be completed with respect to this topology. For example, if k is a field, k [[ X ]], the formal power series ring in one variable over k , is the I -adic completion of k [ X ] where I is the principal ideal generated by X. This ring serves as an algebraic analogue of the disk.