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Definition: Ring delete edit add to favorites [id:683]
vote: please assess correctness correct partially correct not correct please assess preciseness precise partially precise negligent please assess mathematical beauty beautiful, I like it readable boring
Notation
show notation Notation Term LateX Code \((R,+,\cdot)\) ring \((R,+,\cdot)\)
A ring is an algebraic structure \(R\) with two binary inner operations \( + \) and \(\cdot\), denoted by \((R, + ,\cdot)\), for which the following holds:
\((R, + )\) is an Abelian group ,
\((R,\cdot)\) is a semigroup
The distributivity law holds for all \(x,y,z\in R\).
If \((R,\cdot)\) is a monoid (i.e. if the semigroup contains a multiplicative identity), then the ring is called a unit ring (or ring with identity ).
References
[577] Knauer Ulrich: “Diskrete Strukturen - kurz gefasst”, Spektrum Akademischer Verlag, 2001
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Subordinated Structure:
[b] sorted by votes for mathematical beauty [r] sorted by votes for mathematical preciseness [c] sorted by votes for mathematical correctness [v] sorted by views [a] sorted alphabetically [d] sorted by date created [m] sorted by date modified 20 views Ring Homomorphism delete edit 17 views Commutative Ring delete edit
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