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The Natural Partial Order on Regular $$\Gamma $$ Γ -Semigroups

Bulletin of the Malaysian Mathematical Sciences Society, 2015
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Chunse, N., Siripitukdet, M.
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ON THE APPLICABILITY OF FUZZY NATURAL TRANSFORM FOR FUZZY FRACTIONAL-ORDER PARTIAL DIFFERENTIAL PROBLEMS

Fractals, 2023
Being a useful technique for solving differential equation, the study investigated the utility/efficiency of Natural Transform coupled with Adomian Decomposition Method (NADM). For this purpose, one-dimensional (1D) fuzzy fractional-order heat equation was split into two hybrid equations consisting of upper and lower solutions by the fast technique ...
MUHAMMAD USMAN   +3 more
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A Note on Naturally Ordered Semigroups of Partial Transformations Preserving an Equivalence

Bulletin of the Iranian Mathematical Society, 2020
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Quasiresiduals in Semigroups with Natural Partial Order

Algebra Colloquium, 2017
A semigroup (S, ·) is called right (left) quasiresiduated if for any a, b in S there exists x in S such that ax ≤S b (xa ≤S b) with respect to the natural partial order ≤S of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right (left) simplicity of semigroups.
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Naturally Ordered Semigroups of Partial Transformations Preserving an Equivalence Relation

Communications in Algebra, 2013
Let X be a set with |X| ≥3, P(X) the semigroup of all partial transformations on the set X, E be an equivalence relation on X, and Then P E (X) forms a subsemigroup of P(X). In this article, we consider the natural order ≤on P E (X) and determine when two elements of P E (X) are related under this order.
Pei Huisheng, Deng Weina
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THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

Bulletin of the Australian Mathematical Society, 2014
AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups.
Chaopraknoi, Sureeporn   +2 more
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Natural congruences and isomorphism theorems for directed complete partially ordered sets

Algebra universalis, 2017
It was shown by \textit{T. S. Blyth} and \textit{M. F. Janowitz} in [Residuation theory. Oxford etc.: Pergamon Press. (1972; Zbl 0301.06001)] that an equivalence \(R\) on an ordered set is a congruence, i.e. the quotient structure is an ordered set again, if and only if \(R\) is convex. Directed complete partially ordered sets play an important role in
Mahmoudi, Mojgan   +2 more
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Natural Partial Orders on Division Rings with Involution

1993
This article studies intrinsic or natural partial orders on involutive division rings (D,*, II), where (a + b)* = a* + b*, (ab)* = b*a*, a** = a for a, b ∈ D, and where II is the strictly positive cone for an additive partial group order on (D, +). The involution defines several natural multiplicative subgroups G ⊂ D\ 0, and the positive cones are ...
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Classes of semigroups with compatible natural partial order. I.

Mathematica Pannonica, 2011
Summary: In this survey we find new semigroups and collect all semigroups known up to now that have a right (two-sided) compatible natural partial order. In this first part trivially, resp. totally, ordered semigroups are considered and semigroups in special classes -- in particular (E-)medial semigroups -- with this property are studied.
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