Notes on Left Division Systems with Left Unit

1952 ◽  
Vol 74 (3) ◽  
pp. 679 ◽  
Author(s):  
M. F. Smiley
Keyword(s):  
Left Unit

scholarly journals Eight-dimensional real absolute-valued algebras with left unit whose automorphism group is trivial

2003 ◽  
Vol 2003 (70) ◽  
pp. 4447-4454 ◽  
Author(s):  
A. Rochdi
Keyword(s):  
Automorphism Group ◽  
Orthogonal Group ◽  
Isomorphism Problem ◽  
Left Unit

We classify, by means of the orthogonal group𝒪7(ℝ), all eight-dimensional real absolute-valued algebras with left unit, and we solve the isomorphism problem. We give an example of those algebras which contain no four-dimensional subalgebras and characterise with the use of the automorphism group those algebras which contain one.

Some New Class of Absolute Valued Algebras with Left Unit

2010 ◽  
Vol 21 (1) ◽  
pp. 31-40
Author(s):  
M. Benslimane ◽  
A. Moutassim
Keyword(s):  
New Class ◽  
Left Unit

scholarly journals On the Arens product and approximate identity in locally convex algebras

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1493-1496
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Weak Topology ◽  
Approximate Identity ◽  
Arens Product ◽  
Locally Convex Algebras ◽  
Left Unit ◽  
Dual And Bidual ◽  
Locally Convex ◽  
Locally Convex Algebra

Let A' and A'' be the dual and bidual spaces of a locally convex algebra A with dual and weak* topology, respectively. In this paper, we show that A has a bounded right (left) approximate identity if and only if A'' has a right (left) unit with respect to the first (second) Arens product.

scholarly journals Over Absolute Valued Algebras with Central Element not Necassary Idempotent

2017 ◽  
Vol 9 (2) ◽  
pp. 123
Author(s):  
Alassane Diouf ◽  
Andre S. Diabang ◽  
Alhousseynou Ba ◽  
Mankagna A. Diompy
Keyword(s):  
Central Element ◽  
Finite Dimensional ◽  
Left Unit ◽  
The Absolute

We study the absolute valued algebras containing a central element non necessary idempotent. We determine the absolute valued algebras containing a central element if we add some requirements. Also we gives a classification of finite-dimensional absolute valued algebras containing a generalized left unit and central element.

scholarly journals Absolute Valued Algebras with Strongly One Sided Unit

2017 ◽  
Vol 9 (1) ◽  
pp. 32
Author(s):  
Alassane Diouf
Keyword(s):  
Absolute Valued Algebra ◽  
Left Unit ◽  
The Absolute

We classify the absolute valued algebras with strongly left unit of dimension <=. Also we prove that every 8-dimensional absolute valued algebra with strongly left unit contain a 4-dimensional subalgebra, next we determine the form of theirs algebras by the duplication process.

scholarly journals The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 465 ◽  
Author(s):  
Xiaoying Wu ◽  
Xiaohong Zhang
Keyword(s):  
Fuzzy Logic ◽  
Classical Logic ◽  
Special Class ◽  
Maximal Element ◽  
Structure Theorem ◽  
Unit Element ◽  
Fuzzy Logic Systems ◽  
Mathematical Fuzzy Logic ◽  
Left Unit ◽  
Logic Systems

For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Second, the following structure theorem of QM-pseudo-BCI algebra is proved: every QM-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an anti-group pseudo-BCI algebra. Third, the new notion of weak associative pseudo-BCI algebra (WA-pseudo-BCI algebra) is introduced and the following result is proved: every WA-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an Abel group.

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