scholarly journals Semiautomorphic inverse property loops

2016 ◽  
Vol 45 (5) ◽  
pp. 2222-2237 ◽  
Author(s):  
Mark Greer
Keyword(s):  
Inverse Property

THE MOUFANG LAWS, GLOBAL AND LOCAL

2009 ◽  
Vol 08 (04) ◽  
pp. 477-492 ◽  
Author(s):  
J. D. PHILLIPS
Keyword(s):  
Present Author ◽  
Inverse Property ◽  
Loop Theory ◽  
Traditional Definition ◽  
Moufang Loops ◽  
Definition Of ◽  
Global And Local

There are many possible ways to define Moufang element. We show that the traditional definition is not the most felicitious — for instance, the set of all Moufang elements in an arbitrary loop, qua the traditional definition, need not form a subloop. We offer a new definition of Moufang element that ensures that the set of all Moufang elements in an arbitrary loop is a subloop. Moreover, this definition is "maximally algebraic" with respect to autotopisms. We also give an application of this new definition by showing that a flexible A-element in an inverse property loop is, in fact, a Moufang element, thus sharpening a well-known result of Kinyon, Kunen, and the present author [6]. Finally, we prove that divisible, Moufang groupoids are Moufang loops, thus sharpening a result of Kunen [9], one of the first computer-generated proofs in loop theory.

On Weak Inverse Property Loops

1972 ◽  
Vol s2-5 (2) ◽  
pp. 298-302 ◽  
Author(s):  
Pl. Kannappan
Keyword(s):  
Inverse Property

scholarly journals K-loop Structures Raised by the Direct Limits of Pseudo Unitary $U(p, a_{n})$ and Pseudo Orthogonal $O(p, a_{n})$ Groups

2017 ◽  
Vol 9 (5) ◽  
pp. 37
Author(s):  
ALPER BULUT
Keyword(s):  
Relativistic Theory ◽  
Direct Limit ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Inverse Property ◽  
Finite Dimensional ◽  
Direct Limits ◽  
Bol Loop

A left Bol loop satisfying the automorphic inverse property is called a K-loop or a gyrocommutative gyrogroup. K-loops have been in the centre of attraction since its first discovery by A.A. Ungar in the context of Einstein's 1905 relativistic theory. In this paper some of the infinite dimensional K-loops are built from the direct limit of finite dimensional group transversals.

scholarly journals Some algebraic structures on the generalization general products of monoids and semigroups

2020 ◽  
Vol 9 (3) ◽  
pp. 727-737
Author(s):  
Suha Ahmad Wazzan ◽  
Ahmet Sinan Cevik ◽  
Firat Ates
Keyword(s):  
Green’S Relations ◽  
Algebraic Structures ◽  
Extended Version ◽  
Inverse Property ◽  
Green's Relations ◽  
Restriction Semigroup ◽  
General Product

Abstract For arbitrary monoids A and B, in Cevik et al. (Hacet J Math Stat 2019:1–11, 2019), it has been recently defined an extended version of the general product under the name of a higher version of Zappa products for monoids (or generalized general product) $$A^{\oplus B}$$ A ⊕ B $$_{\delta }\bowtie _{\psi }B^{\oplus A}$$ δ ⋈ ψ B ⊕ A and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green’s relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice.

On quasi-irresolute characterization of topological loops

2021 ◽  
Vol 104 (4) ◽  
pp. 003685042110445
Author(s):  
Hanan Alolaiyan ◽  
Kashif Maqbool ◽  
Awais Yousaf ◽  
Abdul Razaq
Keyword(s):  
Relative Topology ◽  
Inverse Property

In this paper, we investigate and explore the properties of quasi-topological loops with respect to irresoluteness. Moreover, we construct an example of a quasi-irresolute topological inverse property-loop by using a zero-dimensional additive metrizable perfect topological inverse property-loop [Formula: see text] with relative topology [Formula: see text].

scholarly journals RIEMANN–HILBERT CORRESPONDENCE FOR MIXED TWISTOR -MODULES

2017 ◽  
Vol 18 (3) ◽  
pp. 629-672 ◽  
Author(s):  
Teresa Monteiro Fernandes ◽  
Claude Sabbah
Keyword(s):  
Derived Category ◽  
Inverse Property ◽  
Holonomic Modules

We introduce the notion of regularity for a relative holonomic ${\mathcal{D}}$-module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961–4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative ${\mathcal{D}}$-modules underlying a regular mixed twistor ${\mathcal{D}}$-module, this functor satisfies the left quasi-inverse property.

scholarly journals Comultiplication on monoids

1997 ◽  
Vol 20 (4) ◽  
pp. 803-811
Author(s):  
Martin Arkowitz ◽  
Mauricio Gutierrez
Keyword(s):  
Free Product ◽  
Free Group ◽  
Free Monoid ◽  
Inverse Property

A comultiplication on a monoidSis a homomorphismm:S→S∗S(the free product ofSwith itself) whose composition with each projection is the identity homomorphism. We investigate how the existence of a comultiplication onSrestricts the structure ofS. We show that a monoid which satisfies the inverse property and has a comultiplication is cancellative and equidivisible. Our main result is that a monoidSwhich satisfies the inverse property admits a comultiplication if and only ifSis the free product of a free monoid and a free group. We call these monoids semi-free and we study different comultiplications on them.

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