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Journal of Algebraic Hyperstructures and Logical Algebras最新文献

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New results on Congruence Boolean Lifting Property 关于同余布尔提升性质的新结果
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-09-26 DOI: 10.52547/hatef.jahla.3.1.3
G. Georgescu
{"title":"New results on Congruence Boolean Lifting Property","authors":"G. Georgescu","doi":"10.52547/hatef.jahla.3.1.3","DOIUrl":"https://doi.org/10.52547/hatef.jahla.3.1.3","url":null,"abstract":"The Lifting Idempotent Property (LIP ) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (MV -algebras, commutative l-groups, BLalgebras, bounded distributive lattices, residuated lattices,etc.), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property (CBLP ) for congruence modular algebras). A lifting ideal of a ring R is an ideal of R fulfilling LIP . In a recent paper, Tarizadeh and Sharma obtained new results on lifting ideals in commutative rings. The aim of this paper is to extend an important part of their results to congruences with CBLP in semidegenerate congruence modular algebras. The reticulation of such algebra will play an important role in our investigations (recall that the reticulation of a congruence modular algebra A is a bounded distributive lattice L(A) whose prime spectrum is homeomorphic with Agliano’s prime spectrum of A). Almost all results regarding CBLP are obtained in the setting of semidegenerate congruence modular algebras having the property that the reticulations preserve the Boolean center. The paper contains several properties of congruences with CBLP . Among the results we mention a characterization theorem of congruences with CBLP . We achieve various conditions that ensure CBLP . Our results can be applied to a lot of types of concrete structures: commutative rings, l-groups, distributive lattices, MV -algebras, BL-algebras, residuated lattices, etc.","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128326594","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}
引用次数: 0
State hyper BE-algebras 状态超be代数
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.1
Xiaoyun Cheng, Xialong Xin
{"title":"State hyper BE-algebras","authors":"Xiaoyun Cheng, Xialong Xin","doi":"10.52547/hatef.jahla.2.3.1","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.1","url":null,"abstract":"","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121196552","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}
引用次数: 0
Implicative soju ideals of BCK-algebras bck代数的隐含烧酒理想
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.3
S. Song
{"title":"Implicative soju ideals of BCK-algebras","authors":"S. Song","doi":"10.52547/hatef.jahla.2.3.3","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.3","url":null,"abstract":"Molodtsov proposed soft set theory to address uncertainty in a parameter manner, and Atanassov introduced intuitionistic fuzzy set which is very useful in providing a flexible model to elaborate uncertainty and vagueness involved in decision making. Using intuitive fuzzy set and soft set, Jun et al. introduced a new notion, ``soju structure'', as a kind of hybrid structure. The concept of implicative soju ideal in BCK-algebra will be introduced and several properties will be investigated in this article. We will discuss the relationship between soju subalgebra, soju ideal, positive implicative soju ideal, commutative soju ideal and implicative soju ideal. Also, characterizations of implicative soju ideal will be established.","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133126233","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}
引用次数: 0
Nearness d-algebras 接近d-algebras
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.6
M. A. Öztürk
{"title":"Nearness d-algebras","authors":"M. A. Öztürk","doi":"10.52547/hatef.jahla.2.3.6","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.6","url":null,"abstract":"","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124701444","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}
引用次数: 0
Spherical fuzzy K-algebras 球面模糊k代数
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.7
M. Akram
{"title":"Spherical fuzzy K-algebras","authors":"M. Akram","doi":"10.52547/hatef.jahla.2.3.7","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.7","url":null,"abstract":"","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121117281","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}
引用次数: 3
Hyper BZ-algebras and semihypergroups 超bz代数与半超群
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.2
Y. Du, Xiaohong Zhang
{"title":"Hyper BZ-algebras and semihypergroups","authors":"Y. Du, Xiaohong Zhang","doi":"10.52547/hatef.jahla.2.3.2","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.2","url":null,"abstract":"In this paper, we introduce the new concept of a hyper BZ-algebra which is a generalization of BZ-algebra and hyper BCI-algebra, and give some examples and basic properties. We discuss the relationships among hyper BZ-algebras, hyper BCC-algebras and hyper BCI-algebra. Moreover, we propose the concepts of anti-grouped hyper BZ-algebras and generalized anti-grouped hyper BZ-algebras, and prove that the following important results:(1) Every anti-grouped hyper BZ-algebra is an anti-grouped BZ-algebra;(2) Every generalized anti-grouped hyper BZ-algebra corresponds to a semihypergroup. Finally, we present a method to construct a new hyper BZ-algebra by using a hyper BCC-algebra and a standard generalized anti-grouped hyper BZ-algebra.","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123013000","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}
引用次数: 0
Minimal prime ideals in hoops 篮筐的最小素数理想
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.9
R. Borzooei, M. Aaly
{"title":"Minimal prime ideals in hoops","authors":"R. Borzooei, M. Aaly","doi":"10.52547/hatef.jahla.2.3.9","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.9","url":null,"abstract":"","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115721177","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}
引用次数: 2
On uni-soft p-semisimple ideals and uni-soft strong ideals in BCI-algebras bci -代数中的单软p-半单理想和单软强理想
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-08-01 DOI: 10.52547/hatef.jahla.2.3.8
H. Harizavi, E. Roh, G. Muhiuddin
{"title":"On uni-soft p-semisimple ideals and uni-soft strong ideals in BCI-algebras","authors":"H. Harizavi, E. Roh, G. Muhiuddin","doi":"10.52547/hatef.jahla.2.3.8","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.8","url":null,"abstract":"","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124849642","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}
引用次数: 0
Two kinds of orthopair soft sets as novel approaches to granular computing based on parametrization 两种正交软集是基于参数化的颗粒计算新方法
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-07-02 DOI: 10.52547/hatef.jahla.2.3.4
M. Ali, M. Shabir, F. Feng
{"title":"Two kinds of orthopair soft sets as novel approaches to granular computing based on parametrization","authors":"M. Ali, M. Shabir, F. Feng","doi":"10.52547/hatef.jahla.2.3.4","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.3.4","url":null,"abstract":"This paper aims at introducing two types of orthopair soft sets, which might serve as novel approaches to granular computing based on parametrization. These generalized soft sets emerge naturally when linguistic parameters are employed to convey uncertainty attached to elements of certain sets. Concepts of uncertainty measures attached to the parameters and the whole orthopair soft sets are presented as well. The proposed uncertainty measures are useful for classifying elements of the set of parameters. Different types of granularity measures associated with parameters are presented and are extended to orthopair soft sets. Collective wisdom is helpful in decision making based on consensus. A numerical example is given to demonstrate how orthopair soft sets can be employed in this regard.","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132069414","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}
引用次数: 0
On $alpha$-solvable fundamental groups 关于$ α $可解的基本群
Journal of Algebraic Hyperstructures and Logical Algebras Pub Date : 2021-05-01 DOI: 10.52547/hatef.jahla.2.2.35
F. Mohammadzadeh, E. Mohammadzadeh
{"title":"On $alpha$-solvable fundamental groups","authors":"F. Mohammadzadeh, E. Mohammadzadeh","doi":"10.52547/hatef.jahla.2.2.35","DOIUrl":"https://doi.org/10.52547/hatef.jahla.2.2.35","url":null,"abstract":"We introduce a specific kind of equivalence relation ${xi^*}_n^{alpha}$ on a fuzzy hypergroup S such that the quotient $S/ {xi^*}_n^{alpha}$, the set of all equivalence classes, is an $alpha$-solvable group. This helps us to introduce the $alpha$-solvable fundamental relation $xi^{*alpha}$. In particular, we obtain an equivalent condition with transitivity of $xi^alpha$.","PeriodicalId":223827,"journal":{"name":"Journal of Algebraic Hyperstructures and Logical Algebras","volume":"371 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121755520","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}
引用次数: 0
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