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Everything about Commutative ring
Algebraic structure
In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Commutative ringA 5-minute orientation
- Skim a recent paper: A system of matrix equations over the commutative quaternion ringInfluential work since 2022
- Pick up a classic book: Commutative ringsThe most-reprinted book on the subject
- Read the landmark paper: Non-commutative geometry and string field theoryCited 1,432 times
- Go sideways: Glossary of commutative algebraA closely related topic
- Go sideways: Glossary of ring theoryA closely related topic
📖 Definitions
Noun A ring whose multiplicative operation is commutative.
🏆 Landmark papers (most cited)
Non-commutative geometry and string field theory
The Zero-Divisor Graph of a Commutative Ring
Coloring of commutative rings
The total graph of a commutative ring
Valuations on a commutative ring
Strongly irreducible ideals of a commutative ring
Coalgebras over a commutative ring
Every Commutative Ring Has a Minimal Ring Extension
🆕 Influential since 2022
📚 Books worth reading
- 📕Commutative ringsIrving Kaplansky, Irving Kaplansky · 1966
Commutative algebraOscar Zariski · 1958- 📕Commutative algebraAron Simis, Giuseppe Valla · 1994
Introduction to commutative algebraMichael Francis Atiyah · 1969- 📕Commutative Ring Theory and ApplicationsMarco Fontana, Salah-Eddine Kabbaj · 2017
Commutative AlgebraIrena Peeva · 2013
Commutative AlgebraMarco Fontana, Sophie Frisch · 2010
Linear algebra over commutative ringsBernard R. McDonald · 1984
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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