Readers should have a background in number theory,

commutative algebra, and the general theory of schemes.

There are important theorems that are commonly treated in advanced books on

commutative algebra without proofs, because the existing proofs are so difficult, say Majadas and Rodicio (both U.

A

commutative algebra X with product x [o] y is called a Jordan algebra if [x.

A Term of

Commutative Algebra by Allan Altman and Steve Kleiman is available in digital and print format; the digital version is available to students free of charge, and the book has been adopted at MIT for the 2012-2013 academic year.

Readers are assumed to know some algebraic and geometric topology and some

commutative algebra.

Exploratory Workshop on Combinatorial

Commutative Algebra and Computer Algebra (2008: Mangalia, Romania) Ed.

For one, by building on the well-studied setting of modules over commutative rings, we get a theory where the considerable power and development of

commutative algebra can be easily brought to bear.

In [MS13a], Manjunath and Sturmfels relate Riemann-Roch theory for finite graphs to Alexander duality in

commutative algebra using this ideal.

Readers are assumed to have a basic knowledge of

commutative algebra, homological algebra, and category theory.

These modules play important roles in various areas of algebra, primarily

commutative algebra, including rings of p-adic integers and certain power series rings over division rings.

The book is suitable for researchers and graduate students interested in combinatorial aspects of

commutative algebra, optimization, discrete geometry, statistics, mirror symmetry, and geometry of numbers.

Coverage includes a guide to closure operations in

commutative algebra, a survey of test ideals, finite-dimensional vector spaces with Frobenius action, finiteness and homological conditions in commutative group rings, regular pullbacks, noetherian rings without finite normalization, Krull dimension of polynomial and power series rings, the projective line over the integers, on zero divisor graphs, and a closer look at non-unique factorization via atomic decay and strong atoms.