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

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...

more general geometrical constructions. Near-field (mathematics) Semiring Near-semiring G. Pilz, (1982), "Near-Rings: What They Are and What They Are Good...

a near-semiring, and some additive monads do qualify as such. However, not all additive monads meet the distributive laws of even a near-semiring. In...

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...

such that α · ω ≤ ωω ≤ (α + 1) · ω. The ordinal numbers form a left near-semiring, but do not form a ring. Hence the ordinals are not a Euclidean domain...

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)...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

all unital rings, maximal ideals are prime. In principal ideal domains a near converse holds: every nonzero prime ideal is maximal. All principal ideal...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

*-invariant: x ∈ I ⇒ x* ∈ I and so on. *-rings are unrelated to star semirings in the theory of computation. A *-algebra A is a *-ring, with involution...

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

unital algebra containing A, in the sense of universal constructions. Semiring Jacobson (1989), pp. 155–156 Noether (1921), p. 30, §1.2 Dorroh (1932)...

nonassociative division algebras such as the octonions are also of interest. A near-field is an algebraic structure similar to a division ring, except that it...

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

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

Distributivity is most commonly found in semirings, notably the particular cases of rings and distributive lattices. A semiring has two binary operations, commonly...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

sense that 0 x = 0 for all x. Near-ring: a semiring whose additive monoid is a (not necessarily abelian) group. Ring: a semiring whose additive monoid is an...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

addition form a semiring, called the min tropical semiring, and a valuation v is almost a semiring homomorphism from K to the tropical semiring, except that...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

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...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...

loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie...