Structural decomposition of finite semigroups
Darapu Umadarapuuma@outlook.comDepartment of Computer Science & EngineeringPragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile → , Khushbookhushboo@niu.edu.inSchool of Fine Arts & DesignNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Huma Khanhuma@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Kotteti Santosh Rupa Manjushaksrmanjusha@outlook.comDepartment of CSE (Artificial Intelligence & Machine Learning)Pragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile → , *Uday Chandrakant PatkarCorresponding authorudaypatkarcomp@gmail.comDepartment of Computer EngineeringBharati Vidyapeeth’s College of EngineeringLavale, Pune, Maharashtra, 412115, IndiaView full profile → , D. Raghavendra Gowdaraghavendragd@outlook.comDepartment of Computer Science and EngineeringVardhaman College of EngineeringShamshabad, Hyderabad, Telangana, 501218, IndiaView full profile → , Suvarna Milind Patilsuvarna.patil1@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3071
- Pages:
- 4535–4546
Abstract
The systematic structure of finite semigroups allows analysis of finite semigroups in terms of inner algebraic structure and behavior. The paper will talk about the decomposition method used on the basis of the relations of Green, ideal theory and idempotent elements to classify the semigroup elements. It concentrates on Rees theorem and its expression in a matrix form of entirely simple semigroups, 0-simple semigroups, which makes it possible to canonically describe the structure. Furthermore, algorithmic techniques are designed to locate ideals, which computes the equivalence classes, an efficient Rees decomposition and factorization. The augmented computational tractability and scaling of large semigroups can be achieved by using the proposed procedures. The experimental analysis shows that the decomposition accuracy and simplification of computations increase. The outcomes are the contribution to the field of the algebraic theory and the use in the automata, cryptography and the discrete optimization systems to ensure high level of structure insight and efficiency in implementation.
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References
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