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Localization (commutative algebra)
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Localization in Algebra
Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.
Surface Analysis: SIMS Examples
Explores surface analysis examples using SIMS, covering segregation, cleaning, and depth profiling of materials.
Primary Decomposition in Commutative Rings
Covers primary decomposition in commutative rings and its application in prime ideals.
Abélianization: Fundamental Groups
Explores abélianization of fundamental groups in commutative spaces with examples and proofs.
Modular Arithmetic: Operations and Properties
Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.
Modular Arithmetic: Properties and Examples
Covers modular arithmetic properties, computation examples, and commutative rings.
Ring Constructions: Structure Theorems
Explores operations on ideals and structure theorems in commutative rings.
Lagrange Theorem: Equivalence Relations
Explores Lagrange's theorem in commutative groups and the concept of equivalence relations, demonstrating their practical applications.
Isomorphism: Order of Group Elements
Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.
Polynomials: Rings and Operations
Covers the basics of polynomials, focusing on rings, operations, and properties.