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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.
For over forty years, Robert Gilmer's numerous articles and books
have had a tremendous impact on research in commutative algebra. It
is not an exaggeration to say that most articles published today in
non-Noetherian ring theory, and some in Noetherian ring theory as
well, originated in a topic that Gilmer either initiated or
enriched by his work. This volume, a tribute to his work, consists
of twenty-four articles authored by Robert Gilmer's 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. In a concluding
article, Robert Gilmer points out directions for future research,
highlighting the open problems in the areas he considers of
importance. Robert Gilmer's article is followed by the complete
list of his published works, his mathematical genealogical tree,
information on the writing of his four books, and reminiscences
about Robert Gilmer's contributions to the stimulating research
environment in commutative algebra at Florida State in the middle
1960s. in a significant and large area of commutative algebra.
Power series provide a technique for constructing examples of
commutative rings. In this book, the authors describe this
technique and use it to analyse properties of commutative rings and
their spectra. This book presents results obtained using this
approach. The authors put these results in perspective; often the
proofs of properties of classical examples are simplified. The book
will serve as a helpful resource for researchers working in
commutative algebra.
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