scholarly journals Some Finiteness Conditions for Strong Semilattice of Semigroups

2017 ◽  
Vol 6 (6) ◽  
pp. 160
Author(s):  
Basri Çalişkan
Keyword(s):  
Finiteness Conditions ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Strong Semilattice Of Semigroups

Strong Semilattices of Implicative Semigroups

2008 ◽  
Vol 15 (01) ◽  
pp. 53-62
Author(s):  
Shuk Yee Lee ◽  
K. P. Shum ◽  
Congxin Wu
Keyword(s):  
Analogous Result ◽  
Practical Method ◽  
Main Difficulty ◽  
Large Size ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Strong Semilattice Of Semigroups

It is well known that a strong semilattice of semigroups is still a semigroup. However, it is not known whether the analogous result carries or not for a strong semilattice of implicative semigroups. The main difficulty is that the implicative operation ∗ is hard to define on the semilattice, especially we need the operation ∗ of the implicative semigroup to be compatible with the negatively ordered relation and the semigroup multiplication on the semilattice of implicative semigroups. In this paper, we provide a practical method of constructing such a strong semilattice of mplicative semigroups. Our method is particularly useful in constructing implicative semigroups of large size. A constructed example is given.

A Structure Theorem of Regular ${\cal H}^\sharp$-Cryptographs

2008 ◽  
Vol 15 (04) ◽  
pp. 653-666 ◽  
Author(s):  
Xiangzhi Kong ◽  
Zhiling Yuan ◽  
K. P. Shum
Keyword(s):  
Structure Theorem ◽  
Abundant Semigroup ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Abundant Semigroups ◽  
Completely Regular Semigroups ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Green Relations ◽  
Strong Semilattice Of Semigroups

A new set of generalized Green relations is given in studying the [Formula: see text]-abundant semigroups. By using the generalized strong semilattice of semigroups recently developed by the authors, we show that an [Formula: see text]-abundant semigroup is a regular [Formula: see text]-cryptograph if and only if it is an [Formula: see text]-strong semilattice of completely [Formula: see text]-simple semigroups. This result not only extends the well known result of Petrich and Reilly from the class of completely regular semigroups to the class of semiabundant semigroups, but also generalizes a well known result of Fountain on superabundant semigroups from the class of abundant semigroups to the class of semiabundant semigroups.

scholarly journals Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Francesco Catino ◽  
Ilaria Colazzo ◽  
Paola Stefanelli
Keyword(s):  
Finite Order ◽  
Algebraic Structure ◽  
Baxter Equation ◽  
Construction Technique ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
New Construction ◽  
Strong Semilattice Of Semigroups

Abstract This paper aims to introduce a construction technique of set-theoretic solutions of the Yang–Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new solutions. In particular, this method turns out to be useful to provide non-bijective solutions of finite order. It is well-known that braces, skew braces and semi-braces are closely linked with solutions. Hence, we introduce a generalization of the algebraic structure of semi-braces based on this new construction technique of solutions.

scholarly journals The strong nil-cleanness of semigroup rings

2020 ◽  
Vol 18 (1) ◽  
pp. 1491-1500
Author(s):  
Yingdan Ji
Keyword(s):  
Inverse Semigroup ◽  
Simple Semigroup ◽  
Semigroup Ring ◽  
Semigroup Rings ◽  
Locally Inverse Semigroup ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Alpha Beta ◽  
Strong Semilattice Of Semigroups

Abstract In this paper, we study the strong nil-cleanness of certain classes of semigroup rings. For a completely 0-simple semigroup M={ {\mathcal M} }^{0}(G;I,\text{Λ};P) , we show that the contracted semigroup ring {R}_{0}{[}M] is strongly nil-clean if and only if either |I|=1 or |\text{Λ}|=1 , and R{[}G] is strongly nil-clean; as a corollary, we characterize the strong nil-cleanness of locally inverse semigroup rings. Moreover, let S={[}Y;{S}_{\alpha },{\varphi }_{\alpha ,\beta }] be a strong semilattice of semigroups, then we prove that R{[}S] is strongly nil-clean if and only if R{[}{S}_{\alpha }] is strongly nil-clean for each \alpha \in Y .

Completely Regular Semigroups with Generalized Strong Semilattice Decompositions

2005 ◽  
Vol 12 (02) ◽  
pp. 269-280 ◽  
Author(s):  
Xiangzhi Kong ◽  
K. P. Shum
Keyword(s):  
Sufficient Conditions ◽  
Normal Band ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Green’S Relation ◽  
Completely Regular Semigroups ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Necessary And Sufficient ◽  
Characterization Theorems

The concept of ρG-strong semilattice of semigroups is introduced. By using this concept, we study Green's relation ℋ on a completely regular semigroup S. Necessary and sufficient conditions for S/ℋ to be a regular band or a right quasi-normal band are obtained. Important results of Petrich and Reilly on regular cryptic semigroups are generalized and enriched. In particular, characterization theorems of regular cryptogroups and normal cryptogroups are obtained.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

Finiteness conditions and relative derived categories

2021 ◽  
Vol 573 ◽  
pp. 270-296
Author(s):  
Lingling Tan ◽  
Dingguo Wang ◽  
Tiwei Zhao
Keyword(s):  
Derived Categories ◽  
Finiteness Conditions

scholarly journals Homological finiteness conditions for a class of metabelian groups

2017 ◽  
Vol 50 (1) ◽  
pp. 17-25
Author(s):  
Peter H. Kropholler ◽  
Joseph P. Mullaney
Keyword(s):  
Finiteness Conditions ◽  
Metabelian Groups

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

Sign in / Sign up

Export Citation Format

Share Document