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Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.


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TL;DR: In this paper, it was shown that a strongly regular 2-homogeneous l-subadditive mapping T is subadditive, where T is a regular l-additive mappings T: → [0,+∞] of a hereditary cone in the space of measurable functions on a measure space.
Abstract: We prove the additivity of regular l-additive mappings T: → [0,+∞] of a hereditary cone in the space of measurable functions on a measure space. Some examples are constructed of non-d-additive l-additive mappings T. The monotonicity of l-additive mappings T: → [0,+∞] is established. The examples are constructed of nonmonotone d-additive mappings T. Let (S, +) be a commutative cancellation semigroup. Given a mapping T: → S, we prove the equivalence of additivity and l-additivity. It is shown that a strongly regular 2-homogeneous l-subadditive mapping T is subadditive. All results are new even in case = L ∞ + .

1 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the general problem of extension of one inverse semigroup by an another inverse semi-complementary semigroup, and showed that any inverse semigram can be reconstructed from its quotient by any congruence.
Abstract: We study the general problem of extension of one inverse semigroup by an another inverse semigroup. Any inverse semigroup can be rebuilt from its quotient by any congruence.

1 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the same implication holds for positive endo-morphisms, which map generators to positive words, also holds for semigroups, and that all implications for positive laws of length 1.
Abstract: 2. Let a semigroup — la bw impl a y a semigroup law u = v in groups. Doesthe same implication hold in semigroups?To show implication of laws in semigroups we can use only so-called positive endo-morphisms, which map generators to positive words. It is shown in [8] (an example atthe end of this paper), that all implications for positive laws of length ^ 5 which holdin groups, also are valid for semigroups. The fac

1 citations

Journal ArticleDOI
TL;DR: In this paper, the generator of a set-valued regularized concave semigroup is introduced and some properties of its properties are investigated under some appropriate conditions, and differentiability of the iteration family is discussed.
Abstract: Abstract In this paper, a set-valued iteration regularized semigroup, i.e. a family { F t } t ≥ 0 ${\\{F^{t}\\}_{t\\geq 0}}$ of set-valued functions for which F s + t ∘ C = F s ∘ F t , F 0 = C , s , t ≥ 0 , $F^{s+t}\\circ C=F^{s}\\circ F^{t},\\quad F^{0}=C,\\quad s,t\\geq 0,$ will be considered, where C is a set-valued function on a closed convex cone in a Banach space. Under some appropriate conditions the generator of a set-valued regularized concave semigroup is introduced and some of its properties are investigated. Also differentiability of the iteration family { C ∘ F t } t ≥ 0 ${\\{C\\circ F^{t}\\}_{t\\geq 0}}$ is discussed.

1 citations

06 Sep 2013
TL;DR: In this paper, it was shown that a cancellative semigroup is embeddable in an inverse semigroup and that a commutative proper *-semigroup is a group.
Abstract: In this paper, it is shown that a cancellative semigroup is embeddable in an inverse semigroup. It is shown that finite proper *-semigroup is regular and any finite commutative proper *-semigroup is a union of groups. Also it is shown that a finite cyclic proper * semigroup is a group while an infinite one is *-embedded in a proper*-group, and any finite maximal proper*- semigroup has a proper *-extension ring. It is shown that there is a nonregular proper *-ring that cannot be *-embedded in any regular proper *-ring. Also it is shown that an Artinian proper *-ring is a finite direct product of matrix rings over skew fields. It is shown that a commutative proper * and cancellative semigroup is *-embeddable in a regular proper *-semigroup.

1 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202224
20216
20206
20193
201810