Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Alam, Noor; Khan, Noor Mohammad; Obeidat, Sofian; Kirmani, Syed Ajaz K.; Ahmad, Jawed

doi:10.1155/2022/2684474

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…In a related direction, Ahanger et al [11] have established the saturation of generalized left [right] regular semigroups. Additionally, Alam et al [12] have identified some saturated classes of H-commutative, left [right] regular semigroups, medial semigroups, and paramedial semigroups Recently, in [13] the authors have identified several saturated classes of structurally regular semigroups. However, the complete identification of all saturated varieties of semigroups is an open problem.…”

Section: Theorem 5 ([6] (Theorem 54))mentioning

confidence: 99%

Saturated Varieties of Semigroups

Nabi,

Alali,

Bano

2023

Symmetry

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The complete characterization of saturated varieties of semigroups remains an unsolved problem. The primary objective of this paper is to make significant progress in this direction. We initially demonstrate that the variety of semigroups defined by the identity axy=ayxa is saturated. The next main result establishes that the variety of semigroups determined by the identity axy=ayax is saturated. Finally, we show that medial semigroups satisfying the identity xy=xyn, where n≥2, are also saturated. These results collectively lead to the conclusion that epis from these saturated varieties are onto. This paper thus offers substantial progress towards the comprehensive characterization of saturated varieties of semigroups.

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Section: Theorem 5 ([6] (Theorem 54))mentioning

confidence: 99%

Saturated Varieties of Semigroups

Nabi,

Alali,

Bano

2023

Symmetry

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Hex-Derived Molecular Descriptors via Generalized Valency-Based Entropies

et al. 2023

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Entropy is a thermodynamic function in chemistry that, based on the number of possible configurations for a given system or process, measures the randomness and disorder of molecules in that system or process. Many problems in arithmetic, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. A topological descriptor also connects certain physical aspects of the underlying chemical substances, in contrast to a topological index, which in chemical graph theory is a numerical representation of a chemical network. When building models for any chemical network, the graph is crucial. Simonraj et al. produced a brand-new category of graphs known as the third kind of hex-derived networks. In our work, we discuss the third class of hex-derived networks, which includes hex-derived networks (HDN 3 ), triangular hex-derived networks (T HDN 3 ), rectangular hex-derived networks (RHDN 3 ), and chain hex-derived networks (CHDN 3 ). We compute exact results for newly defined entropies by utilizing their topological indices based on end vertex degrees.INDEX TERMS Hex-derived network (HDN 3 ), triangular hex-derived network (T HDN 3 ), rectangular hex-derived network (RHDN 3 ) and chain hex-derived network CHDN 3 ).

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Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Cited by 2 publications

References 19 publications

Saturated Varieties of Semigroups

Saturated Varieties of Semigroups

Hex-Derived Molecular Descriptors via Generalized Valency-Based Entropies

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