The idea of homomorphism in various algebraic and fuzzy algebraic structures has been researched by many scholars. In this study, we consider a Fuzzy Lattice and propose a new approach to study the concept of homomorphism on a fuzzy lattice. Some properties of homomorphism on a fuzzy lattice are studied with respect to a fuzzy congruence relation on a fuzzy lattice and the quotient of a fuzzy lattice. Consequently, we construct the first isomorphism theorem of a quotient of fuzzy lattices and apply this theorem to derive the second and third isomorphism theorems. Finally, we establish a one-to-one correspondence between the set of all fuzzy congruence relations which satisfy some condition and the set of all fuzzy congruences on a quotient fuzzy lattice.
{"title":"Homomorphism and isomorphism theorems on fuzzy lattices","authors":"Sileshe Gone Korma, Radhakrishna Kishore Parimi, Dawit Chernet Kifetew","doi":"10.1080/27684830.2023.2255411","DOIUrl":"https://doi.org/10.1080/27684830.2023.2255411","url":null,"abstract":"The idea of homomorphism in various algebraic and fuzzy algebraic structures has been researched by many scholars. In this study, we consider a Fuzzy Lattice and propose a new approach to study the concept of homomorphism on a fuzzy lattice. Some properties of homomorphism on a fuzzy lattice are studied with respect to a fuzzy congruence relation on a fuzzy lattice and the quotient of a fuzzy lattice. Consequently, we construct the first isomorphism theorem of a quotient of fuzzy lattices and apply this theorem to derive the second and third isomorphism theorems. Finally, we establish a one-to-one correspondence between the set of all fuzzy congruence relations which satisfy some condition and the set of all fuzzy congruences on a quotient fuzzy lattice.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.1080/14794802.2023.2239195
G. Gueudet, C. Buteau, Laura Broley, Joyce Mgombelo, E. Muller, A. I. Sacristán, Marisol Santacruz Rodriguez
{"title":"Learning programming for mathematical investigations: an instrumental and community of practice approach","authors":"G. Gueudet, C. Buteau, Laura Broley, Joyce Mgombelo, E. Muller, A. I. Sacristán, Marisol Santacruz Rodriguez","doi":"10.1080/14794802.2023.2239195","DOIUrl":"https://doi.org/10.1080/14794802.2023.2239195","url":null,"abstract":"","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48396689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-30DOI: 10.1080/27684830.2023.2250492
G. Tessema, G. A. Derese, A. Tiruneh
{"title":"Analysis of thermal and surface roughness effects of slider bearing in the case of turbulent lubricant flow using finite element method","authors":"G. Tessema, G. A. Derese, A. Tiruneh","doi":"10.1080/27684830.2023.2250492","DOIUrl":"https://doi.org/10.1080/27684830.2023.2250492","url":null,"abstract":"","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82758046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-19DOI: 10.1080/14794802.2023.2241433
Marloes van Hoeve, M. Doorman, M. Veldhuis
{"title":"Fostering a growth mindset in secondary mathematics classrooms in the Netherlands","authors":"Marloes van Hoeve, M. Doorman, M. Veldhuis","doi":"10.1080/14794802.2023.2241433","DOIUrl":"https://doi.org/10.1080/14794802.2023.2241433","url":null,"abstract":"","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42839461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-05DOI: 10.1080/14794802.2023.2243250
A. Baccaglini-Frank, Giulia Lisarelli
{"title":"The Mathematics Teacher in the Digital Era: International Research on Professional Learning and Practice","authors":"A. Baccaglini-Frank, Giulia Lisarelli","doi":"10.1080/14794802.2023.2243250","DOIUrl":"https://doi.org/10.1080/14794802.2023.2243250","url":null,"abstract":"","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46504133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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