R. Y. Sharp, Steps in commutative algebra (London Mathematical Society Student Texts 19, Cambridge University Press, Cambridge1990) pp. xii + 321, cloth 0 521 39338 8, £30, paper 0 521 39732 4, £10.95. [PDF]
Proceedings of the Edinburgh Mathematical Society, 1992 Patrick F. Smith
openalex +2 more sources
Unified Analytic Solution of Polynomial Equations in Non-Commutative Clifford Algebraic Closure: A Comprehensive Treatment with Complete Mathematical Foundations [PDF]
本文提出了求解多项式方程的微分代数和向量代数框架对非交换克利福德代数设置的全面扩展。我们通过引入一个严格定义的路径排序算子 P，直接面对非交换性带来的基本障碍，该算子 P 投射到对称子空间上，同时保留基本代数结构。我们通过构造非交换克利福德代数闭包 V nc Cl，为求解在非交换克利福德代数 Cl（V， Q） 中定义的多元多项式方程组建立了完整的理论基础。求解方法为此类系统的根提供了显式分析表达式，采用统一形式：非交换牛顿恒等式和收敛分析。开发的算法通过全面的误差分析实现了 O（n 3 m 3 2 3m） 复杂度。数值验证在各种测试用例中展示了 10 −13 残差的精度。这项工作与经典的不可能性结果相协调，同时证明显式解析解存在于适当扩展的代数结构中，这些代数结构在非交换环境中结合了微分和几何运算。
Dongqi Liu, shifa liu
openalex +2 more sources
One functional operator inversion formula
Mathematical Modelling and Analysis, 2001 Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator
P. Plaschinsky
doaj +1 more source
Commutative Algebra (lecture notes, Master in Mathematics, Master in Secondary Education)
, 2022 Gabor Wiese
openalex +1 more source
Unified Analytic Solution of Polynomial Equations in Commutative Clifford Algebraic Closure: A Comprehensive Treatment with Complete Mathematical Foundations [PDF]
Dongqi Liu, shifa liu
openalex +1 more source
CAML: Commutative Algebra Machine Learning─A Case Study on Protein-Ligand Binding Affinity Prediction. [PDF]
J Chem Inf ModelFeng H +6 more
europepmc +1 more source
Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]
Commun Math PhysDorigoni D +7 more
europepmc +1 more source