cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property...

we mention: regular semigroups, orthodox semigroups, semigroups with involution, inverse semigroups and cancellative semigroups. There are also interesting...

apply for the right cancellative or two-sided cancellative properties. In a semigroup, a left-invertible element is left-cancellative, and analogously for...

mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...

notion of nearness Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition. v t e v t e...

Right-cancellative If, for all x, y, z, relation yx = zx implies y = z Cancellative If it is both right-cancellative and left-cancellative A semigroup with...

an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regular semigroups; these are I-semigroups in which...

semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed...

that the word problem for groups is unsolvable, using Turing's cancellation semigroup result.: 354  The proof contains a "Principal Lemma" equivalent...

identity). This means that the cancellative elements of any commutative monoid can be extended to a group. The cancellative property in a monoid is not necessary...

inverse, and is not even a cancellative semigroup because we cannot cancel the 0 in the equation 1·0 = 0·0. This semigroup arises in various contexts...

domain, the multiplication in the wheel no longer results in a cancellative semigroup. The concepts applied to standard arithmetic are similar to those...

satisfied identity (see below). The cancellative semigroups also do not form a variety of algebras, since the cancellation property is not an equation, it...

In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating...

virtue of an equation being a quasi-identity for which n = 0. The cancellative semigroups form a quasivariety. Let K be a quasivariety. Then the class of...

lemma Semigroup Subsemigroup Free semigroup Green's relations Inverse semigroup (or inversion semigroup, cf. [1]) Krohn–Rhodes theory Semigroup algebra...

left inverse is left-cancellative), and every retraction is an epimorphism (every morphism with a right inverse is right-cancellative). In algebra, sections...

groups. Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition. A. V. Arhangelskii. Topological...

the case of any commutative semigroup. Without the cancellation property, the semigroup homomorphism from the semigroup into the group may be non-injective...

completely 0-simple semigroups. All epigroups are also eventually regular semigroups. (also known as π-regular semigroups) A cancellative epigroup is a group...

embedding dualizing the preceding Kimura diagram. Cancellative skew lattices A skew lattice is cancellative if x ∨ y = x ∨ z {\displaystyle x\vee y=x\vee...

domain and S {\displaystyle S} is a torsion-free cancellative GCD-semigroup. A GCD-semigroup is a semigroup with the additional property that for any a {\displaystyle...

Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups". ESAIM Probability & Statistics. 7: 171–208. doi:10.1051/ps:2003001....

uniqueness follow from the fact the Murray-von Neumann semigroup of projections in an AF algebra is cancellative. The counterpart of simple AF C*-algebras in the...

divisibility. In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, an equality ab = ac implies b = c. "Integral...

underlying vector space V ⊕ W with gradation (V ⊕ W)i = Vi ⊕ Wi . If I is a semigroup, then the tensor product of two I-graded vector spaces V and W is another...

finite subsets of an amenable group , and further, of a cancellative left-amenable semigroup. Theorem:—For every measurable subadditive function f : (...

and y be unique can be replaced by the requirement that the magma be cancellative. The unique solutions to these equations are written x = a \ b and y...

their unknowns are erased; as such, they are usually studied over free semigroups. quadratic equations, which are those containing each of their unknowns...

to consider Cayley tables for other algebraic structures, such as for semigroups, quasigroups, and magmas, but some of the properties above do not hold...