semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings...

In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...

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...

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...

In mathematics, in the field of tropical analysis, the log semiring is the semiring structure on the logarithmic scale, obtained by considering the extended...

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)...

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...

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...

generally, all complete semirings are quasiregular. The term closed semiring is actually used by some authors to mean complete semiring rather than just quasiregular...

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...

{\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice...

analysis, tropical analysis is the study of the tropical semiring. The max tropical semiring can be used appropriately to determine marking times within...

\mathbb {T} } denote the tropical semiring and let R = T [ X ] {\displaystyle R=\mathbb {T} [X]} be the polynomial semiring over T {\displaystyle \mathbb...

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...

multiplication, with multiplication distributing over addition. Ring: a semiring whose additive monoid is an abelian group. Division ring: a nontrivial...

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...

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...

multiplication make the natural numbers an instance of a commutative semiring. Semirings are an algebraic generalization of the natural numbers where multiplication...

K , + K , × K ) {\displaystyle (K,+_{K},\times _{K})} be an arbitrary semiring and ( R , ⋅ , ϕ ) {\displaystyle (R,\cdot ,\phi )} a graded monoid. Then...

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...

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...

A + A = A. Tropical analysis – analysis of the idempotent semiring called the tropical semiring (or max-plus algebra/min-plus algebra). Constructive analysis...

Magnus ring over R. Given an alphabet Σ {\displaystyle \Sigma } and a semiring S {\displaystyle S} . The formal power series over S {\displaystyle S}...

requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications...

addition (LogSumExp), giving an isomorphism of semirings between the probability semiring and the log semiring. Logarithmic one-forms df/f appear in complex...

geometric series of elements of abstract algebraic fields, rings, and semirings. The geometric series is an infinite series derived from a special type...

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...

family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton, Zack;...

union) in the algebraic structure itself by the notion of complete star semiring. Wildcard character Glob (programming) It is called "strings" for historical...

·, 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...