Commutative bidifferential algebra
نویسندگان
چکیده
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with biderivation, namely binary operation that is derivation in each argument, here begun, an eye toward geometry corresponding B-varieties. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental are established. Resolving deficiency geometry, theory base extension achieved, it shown dominant B-morphisms admit generic B-fibres. A bidifferential version problem articulated.
منابع مشابه
Commutative Algebra
Introduction 5 0.1. What is Commutative Algebra? 5 0.2. Why study Commutative Algebra? 5 0.3. Acknowledgments 7 1. Commutative rings 7 1.1. Fixing terminology 7 1.2. Adjoining elements 10 1.3. Ideals and quotient rings 11 1.4. The monoid of ideals of R 14 1.5. Pushing and pulling ideals 15 1.6. Maximal and prime ideals 16 1.7. Products of rings 17 1.8. A cheatsheet 19 2. Galois Connections 20 2...
متن کاملCommutative Algebra Notes Introduction to Commutative Algebra Atiyah & Macdonald
and we call A the zero ring denoted by 0. A ring homomorphism is a mapping f of a ring A into a ring B such that for all x, y ∈ A, f(x + y) = f(x) + f(y), f(xy) = f(x)f(y) and f(1) = 1. The usual properties of ring homomorphisms can be proven from these facts. A subset S of A is a subring of A if S is closed under addition and multiplication and contains the identity element of A. The identity ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.07.012