scholarly journals CAYLEY AUTOMATON SEMIGROUPS

2009 ◽  
Vol 19 (01) ◽  
pp. 79-95 ◽  
Author(s):  
VICTOR MALTCEV
Keyword(s):  
Left Zero ◽  
Zero Semigroup ◽  
Left Zero Semigroup ◽  
Automaton Semigroups

In this paper we characterize when a Cayley automaton semigroup is finite, is free, is a left zero semigroup, is a right zero semigroup, is a group, or is trivial. We also introduce dual Cayley automaton semigroups and discuss when they are finite.

Independent domination number in Cayley digraphs of rectangular groups

2018 ◽  
Vol 10 (02) ◽  
pp. 1850024
Author(s):  
Nuttawoot Nupo ◽  
Sayan Panma
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Independent Set ◽  
Left Zero ◽  
Zero Semigroup ◽  
Left Zero Semigroup ◽  
Group A ◽  
Independent Domination ◽  
Independent Dominating Set ◽  
Rectangular Group

Let [Formula: see text] denote the Cayley digraph of the rectangular group [Formula: see text] with respect to the connection set [Formula: see text] in which the rectangular group [Formula: see text] is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. An independent dominating set of [Formula: see text] is the independent set of elements in [Formula: see text] that can dominate the whole elements. In this paper, we investigate the independent domination number of [Formula: see text] and give more results on Cayley digraphs of left groups and right groups which are specific cases of rectangular groups. Moreover, some results of the path independent domination number of [Formula: see text] are also shown.

Hausdorff series in a semigroup ring

2020 ◽  
Vol 30 (04) ◽  
pp. 853-859
Author(s):  
Şehmus Fındık ◽  
Osman Kelekci̇
Keyword(s):  
Identity Element ◽  
Semigroup Ring ◽  
Left Zero ◽  
Zero Semigroup ◽  
Closed Formula ◽  
Semigroup Rings ◽  
Left Zero Semigroup ◽  
The Right

Let [Formula: see text] and [Formula: see text] be the semigroup rings spanned on the right zero semigroup [Formula: see text], and on the left zero semigroup [Formula: see text], respectively, together with the identity element [Formula: see text]. We suggest a closed formula solving the equation [Formula: see text] which is the evolution of the Campbell–Baker–Hausdorff formula given by the Hausdorff series [Formula: see text] where [Formula: see text], in the algebras [Formula: see text] and [Formula: see text].

scholarly journals Certain characterizations of varieties of bands

1988 ◽  
Vol 31 (2) ◽  
pp. 301-319 ◽  
Author(s):  
J. A. Gerhard ◽  
Mario Petrich
Keyword(s):  
Rectangular Band ◽  
Simple System ◽  
Left Zero ◽  
Green’S Relations ◽  
Transformation Semigroups ◽  
Lattice Of Varieties ◽  
Green's Relations ◽  
The World ◽  
New System

The lattice of varieties of bands was constructed in [1] by providing a simple system of invariants yielding a solution of the world problem for varieties of bands including a new system of inequivalent identities for these varieties. References [3] and [5] contain characterizations of varieties of bands determined by identities with up to three variables in terms of Green's relations and the functions figuring in a construction of a general band. In this construction, the band is expressed as a semilattice of rectangular bands and the multiplication is written in terms of functions among these rectangular band components and transformation semigroups on the corresponding left zero and right zero direct factors.

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

scholarly journals Finite AG-groupoid with left identity and left zero

2001 ◽  
Vol 27 (6) ◽  
pp. 387-389 ◽  
Author(s):  
Qaiser Mushtaq ◽  
M. S. Kamran
Keyword(s):  
Commutative Semigroup ◽  
Algebraic Structure ◽  
Zero Element ◽  
Commutative Group ◽  
Left Identity ◽  
Left Zero ◽  
Left Invertive Law

A groupoidGwhose elements satisfy the left invertive law:(ab)c=(cb)ais known as Abel-Grassman's groupoid (AG-groupoid). It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that ifGis a finite AG-groupoid with a left zero then, under certain conditions,Gwithout the left zero element is a commutative group.

On Ore extension and skew power series rings with some restrictions on zero-divisors

2016 ◽  
Vol 16 (09) ◽  
pp. 1750164
Author(s):  
E. Hashemi ◽  
A. As. Estaji ◽  
A. Alhevaz
Keyword(s):  
Power Series ◽  
Left Zero ◽  
Ore Extension ◽  
Series Ring ◽  
Zero Divisors ◽  
Open Questions ◽  
Ore Extensions ◽  
Power Series Rings ◽  
Extension Ring ◽  
The Right

The study of rings with right Property ([Formula: see text]), has done an important role in noncommutative ring theory. Following literature, a ring [Formula: see text] has right Property ([Formula: see text]) if every finitely generated two-sided ideal consisting entirely of left zero-divisors has a nonzero right annihilator. Our results in this paper concerns the right Property ([Formula: see text]) of Ore extensions as well as skew power series rings. We will show that if [Formula: see text] is a right duo ring, then the skew power series ring [Formula: see text] has right Property ([Formula: see text]), when [Formula: see text] is right Noetherian and [Formula: see text]-compatible. Moreover, for a right duo ring [Formula: see text] which is [Formula: see text]-compatible, it is shown that (i) the Ore extension ring [Formula: see text] has right Property ([Formula: see text]) and (ii) [Formula: see text] is right zip if and only if [Formula: see text] is right zip. As a corollary of our results, we provide answers to some open questions related to Property [Formula: see text], raised in [C. Y. Hong, N. K. Kim, Y. Lee and S. J. Ryu, Rings with Property ([Formula: see text]) and their extensions, J. Algebra 315 (2007) 612–628].

scholarly journals Infinite automaton semigroups and groups have infinite orbits

2020 ◽  
Vol 553 ◽  
pp. 119-137 ◽  
Author(s):  
Daniele D'Angeli ◽  
Dominik Francoeur ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter
Keyword(s):  
Automaton Semigroups

On the Set of Zero Divisors of a Topological Ring

1967 ◽  
Vol 10 (4) ◽  
pp. 595-596 ◽  
Author(s):  
Kwangil Koh
Keyword(s):  
Finite Number ◽  
Compact Subset ◽  
Finite Ring ◽  
Left Zero ◽  
Topological Ring ◽  
Compact Ring ◽  
Zero Divisors ◽  
Interesting Corollary

Let R be a topological (Hausdorff) ring such that for each a ∊ R, aR and Ra are closed subsets of R. We will prove that if the set of non - trivial right (left) zero divisors of R is a non-empty set and the set of all right (left) zero divisors of R is a compact subset of R, then R is a compact ring. This theorem has an interesting corollary. Namely, if R is a discrete ring with a finite number of non - trivial left or right zero divisors then R is a finite ring (Refer [1]).

scholarly journals On completely0-simple semigroups

1996 ◽  
Vol 19 (3) ◽  
pp. 507-520 ◽  
Author(s):  
Yue-Chan Phoebe Ho
Keyword(s):  
Simple Semigroup ◽  
Matrix Representation ◽  
Semigroup Ring ◽  
Closed Field ◽  
Zero Semigroup ◽  
Algebraically Closed Field

LetSbe a completely0-simple semigroup andFbe an algebraically closed field. Then for each0-minimal right idealMofS,M=B∪C∪{0}, whereBis a right group andCis a zero semigroup. Also, a matrix representation forSother than Rees matrix is found for the condition that the semigroup ringR(F,S)is semisimple Artinian.

Cycloidal algebras

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Jeong Han ◽  
Hee Kim ◽  
J. Neggers
Keyword(s):  
Binary System ◽  
Golden Section ◽  
Commutative Rings ◽  
Zero Semigroup ◽  
Real Numbers ◽  
The Real ◽  
Finite Algebras ◽  
The Right ◽  
Linear Product

AbstractIn this paper we introduce for an arbitrary algebra (groupoid, binary system) (X; *) a sequence of algebras (X; *)n = (X; ∘), where x ∘ y = [x * y]n = x * [x * y]n−1, [x * y]0 = y. For several classes of examples we study the cycloidal index (m, n) of (X; *), where (X; *)m = (X; *)n for m > n and m is minimal with this property. We show that (X; *) satisfies the left cancellation law, then if (X; *)m = (X; *)n, then also (X; *)m−n = (X; *)0, the right zero semigroup. Finite algebras are shown to have cycloidal indices (as expected). B-algebras are considered in greater detail. For commutative rings R with identity, x * y = ax + by + c, a, b, c ∈ ℝ defines a linear product and for such linear products the commutativity condition [x * y]n = [y * x]n is observed to be related to the golden section, the classical one obtained for ℝ, the real numbers, n = 2 and a = 1 as the coefficient b.

Sign in / Sign up

Export Citation Format

Share Document