CLASSIFICATION OF DIFFERENTIALS IN CERTAIN ALGEBRAS
Keywords:
Differentials, Algebraic structures, Homological algebra, Classification, Mathematical physics.Abstract
This study explores the classification of differentials within specific algebraic structures, providing a comprehensive analysis of their properties, interactions, and applications. Differentials play a fundamental role in various branches of mathematics, including differential geometry, commutative algebra, and homological algebra. By focusing on their behavior in certain algebraic systems, this research categorizes differentials based on linearity, degree, and compatibility with algebraic operations. Furthermore, the paper delves into applications in mathematical physics and computational mathematics, illustrating their interdisciplinary utility. The findings aim to advance understanding in both theoretical and applied contexts.
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References
Bourbaki, N. Algebra I: Chapters 1-3. – New York, Springer, 1989. – P. 432.
Mac Lane, S. Homology. – Berlin, Springer, 1963. – P. 422.
Atiyah, M. F., & Macdonald, I. G. Introduction to Commutative Algebra. – Boston, Addison-Wesley, 1969. – P. 128.
Cartan, H., & Eilenberg, S. Homological Algebra. – Princeton, Princeton University Press, 1956. – P. 390.
Spivak, M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. – Boston, Addison-Wesley, 1965. – P. 146.
Griffiths, P., & Harris, J. Principles of Algebraic Geometry. – New York, Wiley, 1978. – P. 813.
