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2024 | OriginalPaper | Chapter

5. Computing Minimal Free Resolutions over Monomial Semirings with Coefficients in D-A Rings

Authors : Guy Mobouale Wamba, Soda Diop, Djiby Sow

Published in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Publisher: Springer Nature Switzerland

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Abstract

The chapter delves into the study of ideals and their resolutions in commutative algebra and algebraic geometry, focusing on minimal free resolutions over monomial semirings with coefficients in D-A rings. It introduces the concept of Gröbner–Shirshov bases and their application in constructing minimal free resolutions, highlighting the Syzygy Theorem and its role in simplifying the resolution process. The chapter also presents algorithms for computing Gröbner–Shirshov bases and minimal free resolutions, showcasing the practical implementation of these theoretical concepts. Additionally, it provides examples and detailed computations, illustrating the effectiveness of the proposed methods in handling complex algebraic structures. This comprehensive exploration offers valuable insights and tools for researchers and practitioners in the field of computational algebra and ring theory.
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previous chapter On Algebraic Algebras Without Divisors of Zero Satisfying
next chapter Schur Complement and Inequalities of Eigenvalues on Block Hadamard Product
Literature
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Berkesch C; Schreyer F,-O. Syzygies, finite length modules, and random curves. arXiv. 1403.0581 (2014).
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Deepak Kapur and Yongyang Cai: An Algorithm for Computing a Gröbner Basis of a Polynomial Ideal over a Ring avec Zero Divisors. Mathematics in Computer Science. pages 601–634. December 2009;
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Metadata
Title
Computing Minimal Free Resolutions over Monomial Semirings with Coefficients in D-A Rings
Authors
Guy Mobouale Wamba
Soda Diop
Djiby Sow
Copyright Year
2024
Book
Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-66222-5_5

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