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Ideal Theoretic Methods in Commutative Algebra
Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings wi
The Prodigal Heiress
Only one thing stood out: Lexington Natalia Hunter was now an heiress, an heiress to a multi-million-dollar fortune, a mansion on the ocean, a yacht, a limousine—so much luxury, far past her most cherished daydream...She felt as if Christmas had come early this year, only no other Christmas could compare to this. It was her favorite holiday, all the rich colors and food and presents, especially from Aunt Cami. Now Aunt Cami had left her the greatest present she would ever receive: many millions of dollars to live the rest of her life in luxury. Lexi always knew she was meant for more than a mediocre job with a run-of-the-mill salary. Her life was supposed to be full of the finer things. When her Aunt Cami dies and leaves her fortune to Lexi, all of Lexi's hopes and dreams of a high class life become a reality. After buying everything she wants, Lexi becomes bored and soon finds herself partying hard with her new rich friends. Then tragedy strikes. Will her new friends help her pick up the pieces? Can she ever forgive herself for the tragedy that is all her fault? Will Lexi find a greater purpose for living in the lap of luxury and become The Prodigal Heiress?
The November Deep
Nell Fitzgerald O'Donovan is an original Canadian heroine, and coast-to-coast solver of true to life mysteries. Recently widowed, this resourceful, intuitive redhead finds herself at the heart of a plot to destroy the multi-million dollar Canadian Neutrino Project, a giant laboratory two kilometres beneath the Precambrian Shield.
Non-Noetherian Commutative Ring Theory
Commutative Ring Theory emerged as a distinct field of research in math ematics only at the beginning of the twentieth century. It is rooted in nine teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of ac...
Multiplicative Ideal Theory in Commutative Algebra
This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.
Advances in Rings, Modules and Factorizations
Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.
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Galois Theory
A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.
