Variable-basis Categorically-algebraic Dualities by Sergey A. Solovyov

“…Davey, which provides a machinery for obtaining topological representations of algebraic structures. The new setting differs from its predecessor in relying on catalg topology, introduced lately by the author as a new approach to topological structures, which incorporates the majority of both crisp and many-valued developments, ultimately erasing the border between them. …”
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8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign by Mohammad Mazyad Hazzazi, Amer Aljaedi, Zaid Bassfar, Misbah Rani, Tariq Shah

“…Various structures were merged here, namely affine transformation, fractional linear transformation, structure of Klein four-group, and the algebraic structures of the Galois fields, $ GF\left({2}^{4}\right) $ and $ GF\left({2}^{8}\right). $ These structures were utilized to synthesize newly $ 1600 $ robust S-boxes. …”
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Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups by Xiaohong Zhang, Florentin Smarandache, Xingliang Liang

“…From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. …”
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Hyperstructures in Lie-Santilli Admissibility and Iso-Theories by Maria Santilli Ruggero, Thomas Vougiouklis

“…Santilli, in early 90'es, tried to find algebraic structures in order to express his pioneer Lie-Santilli's Theory. …”
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Lifting Elements in Coherent Quantales by George Georgescu

“…The abstract results on lifting elements can be applied to study some Boolean lifting properties in concrete algebraic structures: commutative rings, bounded distributive lattices, residuated lattices, MV-algebras, BL-algebras, abelian l-groups, some classes of universal algebras, etc.…”
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Categorical structures for type theory in univalent foundations by Benedikt Ahrens, Peter LeFanu Lumsdaine, Vladimir Voevodsky

“…In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. …”
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On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations by Christos G. Massouros, Naveed Yaqoob

“…This paper presents the study of algebraic structures equipped with the inverted associativity axiom. …”
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On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices by Hamiyet Merkepçi

“…These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. …”
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Rough Semigroups in Connection with Single Valued Neutrosophi c (∈, ∈)-Ideals by Young Bae Jun, Anas Al-Masarwah, Majdoleen Abuqamar

“…Rough set theory for algebraic structures like semigroups is a formal approximation space consisting of a universal set and an equivalence relation. …”
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Splicing systems over permutation groups of length two by Hamzah, N. Z. A., Mohd. Sebry, N. A., Fong, Wan Heng, Sarmin, NorHaniza, Turaev, S.

“…With several restrictions to splicing rules, the generative power increase up to recursively enumerable languages. Algebraic structures can also be used in order to control the splicing systems. …”
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THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G by Gh. A. Nasiriboroujeni, M. Mirzavaziri, A. Erfanian

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Introduction to NeutroHyperGroups by M.A. Ibrahim, A.A.A. Agboola

“…NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. …”
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Polynomial Distributions and Transformations by Yue Yu, Pavel Loskot

“…Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. …”
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Polyadic Analogs of Direct Product by Steven Duplij

“…We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from different multipliers can be “entangled” such that the product is no longer componentwise. …”
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Pattern graph rewrite systems by Aleks Kissinger, Alex Merry, Matvey Soloviev

“…We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.…”
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Pattern Graph Rewrite Systems by Kissinger, A, Merry, A, Soloviev, M

“…We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.…”

f-Grouplikes by Hooshmand, M. H., Sarmin, Nor Haniza

“…A nice example for associative function,$f$-multiplication and such algebraic structures are $b$-decimal part functions$(\; )_b$, $b$-addition $+_b$, and the real $b$-grouplike $(\mathbb{R},+_b)$.In this paper, we introduce an important type of grouplikes (namely $f$-grouplike) that is motivated fromthe both topics. …”

Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four by Adel Alahmadi, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, Patrick Solé

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Dihedral Group in The Ancient Genetic by Isah Aisah, Eddy Djauhari, Asep Singgih

“…Ancient genetic codes can be reviewed as algebraic structures as a vector spaces and other structures as symmetry groups. …”
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Particle-antiparticle duality and fractionalization of topological chiral solitons by Chang-geun Oh, Sang-Hoon Han, Seung-Gyo Jeong, Tae-Hwan Kim, Sangmo Cheon

“…As a result, such dualities and fractionalizations support the topological $$\mathbb {Z}_4$$ Z 4 algebraic structures. Our findings will inspire researches seeking feasible and promising topological systems, which may lead to new practical applications such as solitronics.…”
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