semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings...
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In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...
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Matrix ring (redirect from Matrix semiring)
only a semiring for Mn(R) to be defined. In this case, Mn(R) is a semiring, called the matrix semiring. Similarly, if R is a commutative semiring, then...
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Module (mathematics) (redirect from Module over a semiring)
modules are still possible. In particular, for any semiring S, the matrices over S form a semiring over which the tuples of elements from S are a module...
22 KB (3,091 words) - 12:09, 26 March 2025
In mathematics, in the field of tropical analysis, the log semiring is the semiring structure on the logarithmic scale, obtained by considering the extended...
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Monus (redirect from Naturally ordered semiring)
Example of a naturally ordered semiring which is not an m-semiring, Mathematics Stack Exchange, retrieved 2016-10-14 Semirings for breakfast, slide 17 Vereschchagin...
9 KB (1,088 words) - 13:15, 26 June 2025
Ring (mathematics) (section Semiring)
The natural numbers (including 0) form an algebraic structure known as a semiring (which has all of the axioms of a ring excluding that of an additive inverse)...
99 KB (13,697 words) - 09:39, 16 June 2025
mathematics, a near-semiring, also called a seminearring, is an algebraic structure more general than a near-ring or a semiring. Near-semirings arise naturally...
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Quasiregular element (redirect from Quasi-regular semiring)
generally, all complete semirings are quasiregular. The term closed semiring is actually used by some authors to mean complete semiring rather than just quasiregular...
12 KB (1,658 words) - 09:31, 14 March 2025
Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set...
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{\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice...
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applies to matrices with entries in a semiring without modification. Matrices of fixed size with entries in a semiring form a commutative monoid Mat ( m...
128 KB (15,699 words) - 03:26, 7 July 2025
\mathbb {T} } denote the tropical semiring and let R = T [ X ] {\displaystyle R=\mathbb {T} [X]} be the polynomial semiring over T {\displaystyle \mathbb...
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analysis, tropical analysis is the study of the tropical semiring. The max tropical semiring can be used appropriately to determine marking times within...
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multiplication, with multiplication distributing over addition. Ring: a semiring whose additive monoid is an abelian group. Division ring: a nontrivial...
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analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the...
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semiring. This is defined in two ways, depending on max or min convention. The min tropical semiring T {\displaystyle \mathbb {T} } is the semiring T...
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multiplication make the natural numbers an instance of a commutative semiring. Semirings are an algebraic generalization of the natural numbers where multiplication...
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K , + K , × K ) {\displaystyle (K,+_{K},\times _{K})} be an arbitrary semiring and ( R , ⋅ , ϕ ) {\displaystyle (R,\cdot ,\phi )} a graded monoid. Then...
16 KB (2,846 words) - 11:38, 24 June 2025
Formal power series (redirect from Formal power series over a semiring)
Magnus ring over R. Given an alphabet Σ {\displaystyle \Sigma } and a semiring S {\displaystyle S} . The formal power series over S {\displaystyle S}...
54 KB (10,139 words) - 21:31, 19 June 2025
A wheel can be regarded as the equivalent of a commutative ring (and semiring) where addition and multiplication are not a group but respectively a commutative...
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A + A = A. Tropical analysis – analysis of the idempotent semiring called the tropical semiring (or max-plus algebra/min-plus algebra). Constructive analysis...
45 KB (4,391 words) - 14:59, 30 June 2025
Shortest path problem (section General algebraic framework on semirings: the algebraic path problem)
approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between...
46 KB (4,790 words) - 00:08, 24 June 2025
requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications...
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geometric series of elements of abstract algebraic fields, rings, and semirings. The geometric series is an infinite series derived from a special type...
34 KB (4,759 words) - 05:38, 19 May 2025
·, 1, 0, ≤) is an ordered semiring; because there is no natural number between 0 and 1, it is a discrete ordered semiring. The axiom of induction is...
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family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton, Zack;...
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union) in the algebraic structure itself by the notion of complete star semiring. Wildcard character Glob (programming) It is called "strings" for historical...
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arg min, corresponding to using the log semiring instead of the max-plus semiring (respectively min-plus semiring), and recovering the arg max or arg min...
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disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean...
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