A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n, the partitions of 3 ...

Commutative algebra and algebraic geometry form a deeply interwoven field that investigates the structure of polynomial rings, their ideals, and the geometric objects defined by these algebraic sets.

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

World Scientific's newly published book A Non-Hausdorff Completion: The Abelian Category of C-complete Left Modules over a Topological Ring, introduces an entirely new invariant in commutative (and ...

Algebra is the discipline of pure mathematics that is concerned with the study of the abstract properties of a set, once this is endowed with one or more operations that respect certain rules (axioms) ...

Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

Transactions of the American Mathematical Society, Vol. 203 (Mar., 1975), pp. 77-85 (9 pages) Let B be a commutative ring with 1, let G be a finite group of automorphisms of B, and let A be the ...