• semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings...
    52 KB (8,021 words) - 20:00, 5 July 2025
  • In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...
    5 KB (728 words) - 04:57, 7 April 2025
  • 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...
    13 KB (1,812 words) - 00:20, 24 September 2024
  • 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...
    6 KB (1,025 words) - 22:15, 28 March 2023
  • 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
  • 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...
    3 KB (392 words) - 11:18, 31 January 2024
  • 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...
    18 KB (2,214 words) - 21:00, 2 July 2025
  • {\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice...
    9 KB (1,428 words) - 02:44, 30 March 2025
  • Thumbnail for Matrix (mathematics)
    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...
    9 KB (1,383 words) - 16:59, 3 December 2024
  • analysis, tropical analysis is the study of the tropical semiring. The max tropical semiring can be used appropriately to determine marking times within...
    2 KB (186 words) - 13:41, 28 May 2025
  • multiplication, with multiplication distributing over addition. Ring: a semiring whose additive monoid is an abelian group. Division ring: a nontrivial...
    21 KB (2,707 words) - 02:10, 7 June 2025
  • 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...
    625 bytes (63 words) - 09:36, 21 October 2023
  • Thumbnail for Tropical geometry
    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...
    28 KB (3,660 words) - 08:20, 15 June 2025
  • Thumbnail for Natural number
    multiplication make the natural numbers an instance of a commutative semiring. Semirings are an algebraic generalization of the natural numbers where multiplication...
    53 KB (5,887 words) - 07:23, 24 June 2025
  • 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
  • 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
  • Thumbnail for Wheel theory
    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...
    8 KB (1,295 words) - 04:59, 20 June 2025
  • Thumbnail for Mathematical analysis
    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
  • Thumbnail for Shortest 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
  • Thumbnail for Matrix multiplication
    requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications...
    41 KB (6,581 words) - 15:09, 5 July 2025
  • 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...
    49 KB (6,478 words) - 03:13, 3 April 2025
  • family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton, Zack;...
    7 KB (1,152 words) - 17:21, 23 June 2024
  • union) in the algebraic structure itself by the notion of complete star semiring. Wildcard character Glob (programming) It is called "strings" for historical...
    6 KB (884 words) - 09:22, 13 May 2025
  • 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...
    33 KB (5,279 words) - 19:53, 29 May 2025
  • disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean...
    12 KB (1,419 words) - 01:16, 15 November 2024