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Tag Archives: integral domains
Commutative Algebra 15
Unique Factorization Through this article and the next few ones, we will explore unique factorization in rings. The inspiration, of course, comes from ℤ. Here is an application of unique factorization. Warning: not all steps may make sense to the … Continue reading
Posted in Advanced Algebra
Tagged integral domains, irreducibles, noetherian, primes, UFDs, unique factorisation
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Commutative Algebra 0
We’re starting a new series on commutative algebra. This has been in the works for way too long, and eventually we just decided to push ahead with it anyway. Most of the articles will be short, and we’ll try to … Continue reading
Posted in Advanced Algebra
Tagged commutative rings, fields, ideals, integral domains, rings
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Introduction to Ring Theory (1)
Recall that in groups, one has only a binary operation *. Rings are algebraic structures with addition and multiplication operations – and consistency is ensured by the distributive property. Definition. A ring R is a set together with two binary operations: … Continue reading
Posted in Notes
Tagged advanced, characteristic, commutative rings, distributive property, division rings, fields, integral domains, quaternions, ring theory, rings, units, zerodivisors
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