In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups provided that the F-subpolygroups considered in them are normal.

The structure of groups which have at most two isomorphism classes of central factors (B2-groups) are investigated. A complete description of B2-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble B2-groups. Also structural information about insoluble B2-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition.

Isomorphism is the process by which organizations become more similar to each other over time. The purpose of this study was to explore how previous research has examined this phenomenon in sports organizations. We used a semi-systematic approach to conduct the research. In conducting and reporting the review we followed the four stages that are outlined by Snyder (2019). A total of 126 articles underwent an abstract review process, from which 26 articles were extracted. Finally, 13 qualitative articles that related to the research objectives were reviewed. We conducted a content analysis of 13 articles on isomorphism in sport. The articles were published in a variety of academic journals between 1990 and 2023. 8 main themes are presented: Type of isomorphism, Mechanism of isomorphism, Consequences of Isomorphism in Sport Organizations, Function of Isomorphism, Strategies for response to pressure, institutional logics, Application of Isomorphism in Sports Organizations, Managing Isomorphism in Sport Organizations. Results showed isomorphism in sport organizations is driven by three primary mechanisms: coercive isomorphism, mimetic isomorphism, and normative isomorphism. In conclusion, isomorphism is a complex phenomenon that can have both positive and negative consequences for sport organizations. By understanding the mechanisms of isomorphism and carefully managing its effects, sport organizations can leverage its benefits while maintaining their strategic autonomy and fostering a culture of innovation and adaptation.

In this paper, we embark on an in-depth exploration of the profound connections between congruences, ideals, and homomorphisms in Hilbert algebras. Our research unveils a groundbreaking theorem that seamlessly integrates the principles of the first, second, and third isomorphism theorems within this algebraic structure. The study of these isomorphism theorems is crucial, as they provide fundamental insights into the structure and behaviour of algebraic systems, facilitating a deeper understanding and broader applications. This pivotal discovery not only enhances our comprehension of Hilbert algebras but also sets the stage for the development of new and innovative isomorphism theorems, promising to significantly enrich the field.

Here, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as K-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as K-algebras. Based on an explicit K-algebra isomorphism of two Stanley-Reisner rings, or facet rings or edge rings, we present a fast algorithm to find explicitly the isomorphism of the associated simplicial complexes, or graphs.

If companies seek survival and the achievement of their objectives, they must adapt to their normative environments. This study suggests that in the context of isomorphism, when companies interact, they tend to influence each other’s behaviors and actions within their social bounds. In this regard, companies initially joined sustainable development as a response to external pressures and criticisms from governmental institutions and civil society organizations, which blame businesses for environmental degradation. The process of isomorphism explains why companies eventually change in line with uncertainties in behaviors and actions due to collective entanglement. In response to social changes in society, social networks consistently play a prominent role in defining, forecasting, responding to, and adapting to global, social, and environmental changes. Therefore, sustainable development is an example of such a global change. Consequently, this research examines the effect of mimetic isomorphism in the implementation of sustainable development, and the results of structural equation modeling indicate that all three measured dimensions of sustainable development—environmental, social, and corporate governance—are significantly influenced by mimetic isomorphism. Additionally, the findings of these studies suggest strong evidence of the operationalization of sustainable development due to mimetic isomorphism.

The concepts of L-convex systems and Scott-hull spaces are pro-posed on frame-valued setting. Also, we establish the categorical isomorphism between L-convex systems and Scott-hull spaces. Moreover, it is proved that the category of L-convex structures is bireflective in the category of L-convex systems. Furthermore, the quotient systems of L-convex systems are studied.