Ebook: Approximation Theorems in Commutative Algebra: Classical and Categorical Methods

Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc.
Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups.
Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic.
For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.

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Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Approximation Theorems for Valuations on Fields....Pages 3-48
Valuations on Commutative Rings....Pages 49-125
Ordered Groups and Homomorphisms....Pages 127-157
Approximation Theorems for Multi-Structures....Pages 159-207
Front Matter....Pages 209-209
Categorical Logic....Pages 211-261
Approximation Theorems in Categories....Pages 263-305
Back Matter....Pages 307-330

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Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Approximation Theorems for Valuations on Fields....Pages 3-48
Valuations on Commutative Rings....Pages 49-125
Ordered Groups and Homomorphisms....Pages 127-157
Approximation Theorems for Multi-Structures....Pages 159-207
Front Matter....Pages 209-209
Categorical Logic....Pages 211-261
Approximation Theorems in Categories....Pages 263-305
Back Matter....Pages 307-330
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