979 research outputs found
RIGHT PURE UNI-SOFT IDEALS OF ORDERED SEMIGROUPS
In this paper, we initiate the study of pure uni-soft ideals in ordered semigroups. The soft version of right pure ideals in ordered semigroups is considered which is an extension of the concept of right pure ideal in ordered semigroups. We also give the main result for right pure uni-soft ideals in ordered semigroups and characterize right weakly regular ordered semigroups in terms of right pure uni-soft ideals
Tensor products and regularity properties of Cuntz semigroups
The Cuntz semigroup of a C*-algebra is an important invariant in the
structure and classification theory of C*-algebras. It captures more
information than K-theory but is often more delicate to handle. We
systematically study the lattice and category theoretic aspects of Cuntz
semigroups.
Given a C*-algebra , its (concrete) Cuntz semigroup is an object
in the category of (abstract) Cuntz semigroups, as introduced by Coward,
Elliott and Ivanescu. To clarify the distinction between concrete and abstract
Cuntz semigroups, we will call the latter -semigroups.
We establish the existence of tensor products in the category and study
the basic properties of this construction. We show that is a symmetric,
monoidal category and relate with for
certain classes of C*-algebras.
As a main tool for our approach we introduce the category of
pre-completed Cuntz semigroups. We show that is a full, reflective
subcategory of . One can then easily deduce properties of from
respective properties of , e.g. the existence of tensor products and
inductive limits. The advantage is that constructions in are much easier
since the objects are purely algebraic.
We also develop a theory of -semirings and their semimodules. The Cuntz
semigroup of a strongly self-absorbing C*-algebra has a natural product giving
it the structure of a -semiring. We give explicit characterizations of
-semimodules over such -semirings. For instance, we show that a
-semigroup tensorially absorbs the -semiring of the Jiang-Su
algebra if and only if is almost unperforated and almost divisible, thus
establishing a semigroup version of the Toms-Winter conjecture.Comment: 195 pages; revised version; several proofs streamlined; some results
corrected, in particular added 5.2.3-5.2.
Intuitionistic fuzzy soft ordered ternary semigroups
Abstract: In this paper, we introduced the notion of intuitionistic fuzzy soft ideals over an ordered ternary semigroup and their basic properties are investigated
Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups
The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-soft r-ideals are investigated. Using the notions of union-soft l-ideals and union-soft r-ideals, conditions for an ordered semigroup to be regular are considered. The concepts of concave soft sets and critical soft points are introduced, and their properties are discussed
Finite Computational Structures and Implementations
What is computable with limited resources? How can we verify the correctness
of computations? How to measure computational power with precision? Despite the
immense scientific and engineering progress in computing, we still have only
partial answers to these questions. In order to make these problems more
precise, we describe an abstract algebraic definition of classical computation,
generalizing traditional models to semigroups. The mathematical abstraction
also allows the investigation of different computing paradigms (e.g. cellular
automata, reversible computing) in the same framework. Here we summarize the
main questions and recent results of the research of finite computation.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version
published by IEEE Computer Societ
Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach
In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing
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Abstract bivariant Cuntz semigroups
We show that abstract Cuntz semigroups form a closed symmetric
monoidal category. Thus, given Cuntz semigroups S and T, there is another
Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to
C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as
the target in analogues of the UCT for bivariant theories of Cuntz semigroups.
Abstract bivariant Cuntz semigroups are computable in a number of interesting
cases. We explore its behaviour under the tensor product with the Cuntz
semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra.
We also show that order-zero maps between C*-algebras naturally define
elements in the respective bivariant Cuntz semigroup
Abstract bivariant Cuntz semigroups
We show that abstract Cuntz semigroups form a closed symmetric
monoidal category. Thus, given Cuntz semigroups S and T, there is another
Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to
C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as
the target in analogues of the UCT for bivariant theories of Cuntz semigroups.
Abstract bivariant Cuntz semigroups are computable in a number of interesting
cases. We explore its behaviour under the tensor product with the Cuntz
semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra.
We also show that order-zero maps between C*-algebras naturally define
elements in the respective bivariant Cuntz semigroup
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