From the reviews of the first edition:
"It is certainly no exaggeration to say that A Singular
Introduction to Commutative Algebra aims to lead a further stage in
the computational revolution in commutative algebra . Among the
great strengths and most distinctive features is a new, completely
unified treatment of the global and local theories. making it one
of the most flexible and most efficient systems of its
type....another strength of Greuel and Pfister's book is its
breadth of coverage of theoretical topics in the portions of
commutative algebra closest to algebraic geometry, with algorithmic
treatments of almost every topic....Greuel and Pfister have written
a distinctive and highly useful book that should be in the library
of every commutative algebraist and algebraic geometer, expert and
novice alike."
J.B. Little, MAA, March 2004
The second edition is substantially enlarged by a chapter on
Groebner bases in non-commtative rings, a chapter on characteristic
and triangular sets with applications to primary decomposition and
polynomial solving and an appendix on polynomial factorization
including factorization over algebraic field extensions and
absolute factorization, in the uni- and multivariate case."
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