Two Open Problems on CA-Groupoids and Cancellativities of T2CA-Groupoids

An, Xiaogang; Zhang, Xiaohong; Ma, Zhirou

doi:10.3390/axioms11040169

Cited by 3 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we mainly talk about the various transposition regular AG-groupoids. We can discuss the relationships among transposition regular AG-groupoids, hypersemigroups and T2CA-groupoids as well as non-classical logical algebras (see [24][25][26][27][28]).…”

Section: Discussionmentioning

confidence: 99%

Transposition Regular AG-Groupoids and Their Decomposition Theorems

Zhang

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce transposition regularity into AG-groupoids, and a variety of transposition regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties and structures are discussed by their decomposition theorems: (1) L1/R1-transposition regular AG-groupoids are equivalent to each other, and they can be decomposed into the union of disjoint Abelian subgroups; (2) L1/R1-transposition regular AG-groupoids are LR-transposition regular AG-groupoids, and an example is given to illustrate that not every LR-transposition regular AG-groupoid is an L1/R1-transposition regular AG-groupoid; (3) an AG-groupoid is an L1/R1-transposition regular AG-groupoid if it is an LR-transposition regular AG-groupoid satisfying a certain condition; (4) strong L2/R3-transposition regular AG-groupoids are equivalent to each other, and they are union of disjoint Abelian subgroups; (5) strong L3/R2-transposition regular AG-groupoids are equivalent to each other and they can be decomposed into union of disjoint AG subgroups. Their relations are discussed. Finally, we introduce various transposition regular AG-groupoid semigroups and discuss the relationships among them and the commutative Clifford semigroup as well as the Abelian group.

show abstract

Section: Discussionmentioning

confidence: 99%

Transposition Regular AG-Groupoids and Their Decomposition Theorems

Zhang

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In semigroups and other groupoids, scholars have studied quasi-separativity and separativity by establishing certain congruences in order to further reveal their intrinsic properties [21][22][23]. We will now discuss the quasi-separativity on the left transposition regular TA-groupoids.…”

Section: Corollarymentioning

confidence: 99%

Transposition Regular TA-Groupoids and Their Structures

Zhang

2022

Axioms

Self Cite

View full text Add to dashboard Cite

Tarski associative groupoid (TA-groupoid) is a kind of non-associative groupoid satisfying Tarski associative law. In this paper, the new notions of transposition regular TA-groupoid are proposed and their properties and structural characteristics are studied by using band and quasi-separativity. In particular, the following conclusions are strictly proved: (1) every left transposition regular TA-groupoid is a semigroup; (2) every left transposition regular TA-groupoid is the disjoint union of sub Abelian groups; and (3) a finite TA-groupoid with quasi-separativity and a finite left transposition regular TA-groupoid are equivalent.

show abstract

On type-2 cyclic associative groupoids and inflationary pseudo general residuated lattices

An,

Chen

2024

IFS

View full text Add to dashboard Cite

This paper explores the relationship between fuzzy logic algebra and non associative groupoid. As a groupoid which can satisfy type-2 cyclic associative (T2CA) law, T2CA-groupoid is characterized by generalized symmetry. Fuzzy logic algebra is a major direction in the study of fuzzy logic. Residuated lattices are a class of fuzzy logic algebras with widespread applications. The inflationary pseudo general residuated lattice (IPGRL), a generalization of the residuated lattice, does not need to satisfy the associative law and commutative law. Moreover, the greatest element of IPGRL is no longer the identity element. In this paper, the notion of T2CA-IPGRL (IPGRL in T2CA-groupoid) is proposed and its properties are investigated in combination with the study of IPGRL and T2CA-groupoid. In addition, the generalized symmetry and regularity of T2CA-groupoid are investigated based on the characteristics of commutative elements. Meanwhile, the decomposition of T2CA-root of band with T2CA-unipotent radical is studied as well. The result shows that every T2CA-root of band is the disjoint union of T2CA-unipotent radicals.

show abstract

Two Open Problems on CA-Groupoids and Cancellativities of T2CA-Groupoids

Cited by 3 publications

References 22 publications

Transposition Regular AG-Groupoids and Their Decomposition Theorems

Transposition Regular AG-Groupoids and Their Decomposition Theorems

Transposition Regular TA-Groupoids and Their Structures

On type-2 cyclic associative groupoids and inflationary pseudo general residuated lattices

Contact Info

Product

Resources

About