Maximal semilattice quotient information

In abstract algebra, a branch of mathematics, a maximal semilattice quotient is a commutative monoid derived from another commutative monoid by making...

finest congruence ~ such that the quotient of S by this equivalence relation is a semilattice. Denoting this semilattice by L, we get a homomorphism f from...

Neumann regular ring. Then the (∨,0)-semilattices Idc R and Conc L(R) are both isomorphic to the maximal semilattice quotient of V(R). Bergman proves in a well-known...

to division and produce quotients. Three quotients are exhibited here: left residual, right residual, and symmetric quotient. The left residual of two...

domains. The zero ring (the ring in which 0 = 1 {\displaystyle 0=1} ). The quotient ring Z / m Z {\displaystyle \mathbb {Z} /m\mathbb {Z} } when m is a composite...

semigroup) and idempotents commute (that is, the idempotents of S form a semilattice). Every L {\displaystyle {\mathcal {L}}} -class and every R {\displaystyle...

both belong to F. Then ~ is an equivalence relation; we write H/F for the quotient set. There is a unique Heyting algebra structure on H/F such that the canonical...

the property of being an Alexandrov-discrete space is preserved under quotients. Alexandrov-discrete spaces are named after the Russian topologist Pavel...

E} a preordered vector space. Item 3 says that the preorder is a join semilattice. Because the preorder is compatible with the vector space structure,...

maximal ideals (in contrast, in general, a Jacobson radical is the intersection of all left maximal ideals or the intersection of all right maximal ideals...

one-to-one correspondence between the points of an algebraic variety, and the maximal ideals of its coordinate ring. This correspondence has been enlarged and...

a quotient and a remainder of the division (or Euclidean division) of a by b. In contrast with the case of integers and polynomials, the quotient is...

rings and prime ideals (of ring theory), or distributive lattices and maximal ideals (of order theory). This article focuses on prime ideal theorems...

one-to-one correspondence with the family of all proper cones that are maximal under set inclusion. A total vector ordering cannot be Archimedean if its...

abelian group is normal, so each subgroup gives rise to a quotient group. Subgroups, quotients, and direct sums of abelian groups are again abelian. The...

localization with respect to every maximal ideal is zero. In contrast, the "integrally closed" does not pass over quotient, for Z[t]/(t2+4) is not integrally...

that all maximal chains in P have the same (finite) length. This suffices, since any pair of maximal chains in [Ô, x] can be extended by a maximal chain...

not enough to ask that all the maximal ideals are finitely generated, as there is a non-Noetherian local ring whose maximal ideal is principal (see a counterexample...

\left(R\setminus \left\{0\right\}\right)^{-1}R} is a field, called the quotient field of R {\displaystyle R} . Many of the following notions also exist...

Using this relation, it is possible to construct a partial order on the quotient set of the equivalence, S / ∼ , {\displaystyle S/\sim ,} which is the set...

rational points. Every cyclically ordered group can be expressed as a quotient L / Z, where L is a linearly ordered group and Z is a cyclic cofinal subgroup...

are exactly the bounded distributive lattices with unique minimal and maximal element (which then are the units). Heyting algebras are such semirings...

property: a Noetherian domain R {\displaystyle R} is Dedekind iff for every maximal ideal M {\displaystyle M} of R {\displaystyle R} the localization R M {\displaystyle...

{\displaystyle X,} and ≤ {\displaystyle \leq } induces a wellordering on the quotient X / ∼ . {\displaystyle X/{\sim }.} The order-type of this induced wellordering...