Sign-In
Cart
Four Functors. The 'ancestor' of Mundici's equivalence between unital commutative l-groups and MV algebras
Paperback
ISBN13: 9781848904965
Publisher: College Publications
Published: Oct 1 2025
Pages: 332
Weight: 1.03
Height: 0.69 Width: 6.14 Depth: 9.21
Language: English
Daniele Mundici has proved in 1986 that the category of lattice-ordered commutative groups with strong unit (or unital commutative l-groups, for short) is equivalent to the category of MV algebras, by proving the existance of the quasi-inverse functors Gamma and Xi. He has made the proof in one step, but the proof can be made in two steps, as it is sketched in this book, by introducing the intermediary category of positive-unital commutative l-groups and four functors.
Marco Abbadini has presented in 2021 his equivalence à la Mundici for commutative l-monoids, in two steps, with four functors.
Afrodita Iorgulescu has introduced and studied in 2020 a new commutative framework, centered on m-BCK algebras, containing the commutative groups and the MV algebras. Hence, she has had sufficient background material to generalize Mundici's equivalence, to fi nd its 'ancestor'. The role of unital commutative l-groups is played by the strong mo-ME structures, the role of positive unital commutative l-groups is played by the strong mo-ME positive cones, and the role of MV algebras is played by the XY algebras, all belonging to this new framework. She presents in this book this 'ancestor', in two steps, with four functors: the category of strong mo-ME structures is not equivalent to the category of strong mo-ME positive cones (step 1), but
the category of strong mo-ME positive cones is equivalent to the category of XY algebras (step 2).
Abbadini's results and the wonderful instrument which is Prover9-Mace4 were of major help in writing this book.
Also from
Iorgulescu, Afrodita
Non-commutative Algebras. Pseudo-BCK Algebras versus m-pseudo-BCK Algebras
Iorgulescu, Afrodita
Hardcover
Also in
Algebra
Regents Exams and Answers: Algebra II, Fifth Edition (Barron's New York Regents)
Rubinstein, Gary Michael
Paperback
Regents Exams and Answers: Algebra I, Fifth Edition, (Barron's New York Regents)
Rubinstein, Gary M.
Paperback
Let's Review Regents: Algebra II, Fifth Edition (Barron's New York Regents)
Rubenstein, Gary M., M. S.
Paperback
Pre Algebra Doodle Notes: a complete course of brain-based interactive guided visual notes for Middle School Math Concepts
Danziger, Brigid
Giraffe, Math
Paperback
6th and 7th Grade Math Workbook: Math Practice Book for Grade 6 and 7 [New Edition Includes 900] Practice Questions]
Apex Test Prep
Paperback
Mechanical Engineering for Makers: A Hands-On Guide to Designing and Making Physical Things
Bunnell, Brian
Najia, Samer
Paperback
Summit Math Algebra 1 Book 5: Factoring Polynomials and Solving Quadratic Equations
Joujan, Alex
Paperback
Mathematical Foundations of Quantum Computing: A Scaffolding Approach
Lee, Peter
Yu, James
Cheng, Ran
Hardcover
Basic Math & Pre-Algebra: 1001 Practice Problems for Dummies (+ Free Online Practice)
Zegarelli, Mark
Paperback
Basic Math Refresher for Adults - A Math Workbook with Practice Problems and Online Video Tutorials: [2nd Edition]
Bowling, Matthew
Paperback
HSPT Full Prep Book for Catholic High Schools: Be ready and fearless! Detailed answer explanations
Johnson, Henry N.
Paperback
Math for Programmers: 3D Graphics, Machine Learning, and Simulations with Python
Orland, Paul
Paperback
Dilation and Model Theory for Pairs of Commuting Contraction Operators
Ball, Joseph A.
Sau, Haripada
Hardcover
Graph Paper Notebook: Beautiful Pink Marble and Rose Gold 8 x 10 inches - 5 x 5 Squares per inch, Quad Ruled Cute Graph Paper Composition No
Blush Marble Notebooks
Paperback
Math Fundamentals 2 - Algebra: For Middle School - A Quickstudy Laminated Reference Guide
LLC
Warren, Peggy
Wright, Susan
Other
Math Geek: From Klein Bottles to Chaos Theory, a Guide to the Nerdiest Math Facts, Theorems, and Equations
Rosen, Raphael
Paperback
Mathematics: Its Content, Methods and Meaning
Lavrent'ev, M. a.
Aleksandrov, A. D.
Kolmogorov, A. N.
Paperback
Pre-Algebra for Beginners: The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test
Nazari, Reza
Paperback
Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis
Klein, Felix
Paperback
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Little, John
O'Shea, Donal
Cox, David A.
Hardcover
Topics in Number Theory, Volumes I and II
Leveque, William J.
Mathematics
Leveque, William Judson
Paperback
Mathematical Foundations of Quantum Computing: A Scaffolding Approach
Lee, Peter
Yu, James
Cheng, Ran
Paperback
4th Grade Math Workbook: 1500+ Practice Questions for Daily Exercise [Math Workbooks Grade 4]
Apex Test Prep
Paperback
No-Nonsense Algebra, 2nd Edition: Part of the Mastering Essential Math Skills Series
Fisher, Richard W.
Paperback
Radical Equations: Civil Rights from Mississippi to the Algebra Project
Moses, Robert
Cobb, Charles E.
Paperback
ACCUPLACER Math Prep: ACCUPLACER Math Test Study Guide with Two Practice Tests [Includes Detailed Answer Explanations]
Tpb Publishing
Paperback
Algebra II: 1001 Practice Problems for Dummies (+ Free Online Practice)
Sterling, Mary Jane
Paperback
Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger
Samuel, Pierre
Paperback
Basic Mathematics for Adult Beginners: An Easy Math Refresher Guide for Adults Restarting Their Education Journey
E. Thompson, Charles
Paperback