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Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, commutative rings, module and ring theory, and topological algebraic structures-providing more than 600 current references and 570 display equations for further exploration of the topic.

Abelian groups. --- Rings (Algebra) --- Modules (Algebra) --- Commutative groups --- Group theory --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Algebraic rings --- Ring theory --- Algebraic fields

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This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years.  Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals.  Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.

Algebra. --- Factorization (Mathematics). --- Integral domains. --- Mathematics. --- Factorization (Mathematics) --- Integral domains --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Domains, Integral --- Entire rings --- Rings without zero divisors --- Algebraic geometry. --- Commutative algebra. --- Commutative rings. --- Number theory. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Number Theory. --- Rings (Algebra) --- Geometry, algebraic. --- Number study --- Numbers, Theory of --- Algebraic geometry --- Geometry --- Mathematical analysis