Mutation of permutations corresponds to flip of triangulations. We give, in this article, an interpretation of mutation as a metric on the permutation group $S_n$. Using this metric, we characterize a class of permutations called singular permutations. We also establish a connection with Cayley graphs in the sense of its automorphism group. Received: July 17, 2023Revised: September 20, 2023Accepted: October 18, 2023
{"title":"MUTATION AS METRIC ON PERMUTATION GROUP Sn","authors":"Kodjo Essonana Magnani","doi":"10.17654/0972555523026","DOIUrl":"https://doi.org/10.17654/0972555523026","url":null,"abstract":"Mutation of permutations corresponds to flip of triangulations. We give, in this article, an interpretation of mutation as a metric on the permutation group $S_n$. Using this metric, we characterize a class of permutations called singular permutations. We also establish a connection with Cayley graphs in the sense of its automorphism group. Received: July 17, 2023Revised: September 20, 2023Accepted: October 18, 2023","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"12 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634368","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}
Let $p>2$ be a Sophie Germain prime which means that $q=2 p+1$ is also a prime. Let $K=mathbb{Q}(sqrt{-q})$ and denote its ideal class number by $h_K$. We use Kummer congruences and Bernoulli numbers to study the relation between $p$ and $h_K$. We prove that $-h_K equiv k cdot p(bmod q)$ for some positive integer $k$. Received: August 29, 2023Accepted: October 7, 2023
假设$p>2$是Sophie Germain质数，也就是说$q=2 p+1$也是质数。设$K=mathbb{Q}(sqrt{-q})$，并用$h_K$表示它的理想类数。我们利用Kummer同余和Bernoulli数研究了$p$和$h_K$之间的关系。我们证明了$-h_K equiv k cdot p(bmod q)$对于某个正整数$k$。收稿日期:2023年8月29日。收稿日期:2023年10月7日
{"title":"NOTE ON THE CLASS NUMBER OF IMAGINARY QUADRATIC NUMBER FIELDS AND SOPHIE GERMAIN PRIMES","authors":"Anly Li","doi":"10.17654/0972555523027","DOIUrl":"https://doi.org/10.17654/0972555523027","url":null,"abstract":"Let $p>2$ be a Sophie Germain prime which means that $q=2 p+1$ is also a prime. Let $K=mathbb{Q}(sqrt{-q})$ and denote its ideal class number by $h_K$. We use Kummer congruences and Bernoulli numbers to study the relation between $p$ and $h_K$. We prove that $-h_K equiv k cdot p(bmod q)$ for some positive integer $k$. Received: August 29, 2023Accepted: October 7, 2023","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636237","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}
In this paper, we present a modified cryptographic technique based on the use of recursive matrices as the key in ECC and ElGamal. For encryption, we take into account mapping similar to [5] and the ElGamal technique, in which a plaintext matrix is built from points that correspond to the letters on elliptic curves. The extended generalized Fibonacci matrices, which are a sequence of matrices, have been considered in the creation of key space. The consideration of extended generalized Fibonacci matrices is delightful because it just requires four parameters (integers) as opposed to all of the matrix entries. Our suggested system has a vast key space and is more effective because of the use of a recursive matrix. As a result, it minimizes the complexity of both time and space. Additionally, it is secure and robust since it is based on the challenging number theory issue known as the elliptic curve-discrete logarithm issue. Received: July 4, 2023Revised: September 15, 2023Accepted: September 26, 2023
{"title":"IMPLEMENTATION OF EXTENDED GENERALIZED FIBONACCI MATRICES AS A KEY IN MODIFIED ELLIPTIC CURVE CRYPTOGRAPHY","authors":"Vaishali Billore, Naresh Patel, Hemant Makwana","doi":"10.17654/0972555523025","DOIUrl":"https://doi.org/10.17654/0972555523025","url":null,"abstract":"In this paper, we present a modified cryptographic technique based on the use of recursive matrices as the key in ECC and ElGamal. For encryption, we take into account mapping similar to [5] and the ElGamal technique, in which a plaintext matrix is built from points that correspond to the letters on elliptic curves. The extended generalized Fibonacci matrices, which are a sequence of matrices, have been considered in the creation of key space. The consideration of extended generalized Fibonacci matrices is delightful because it just requires four parameters (integers) as opposed to all of the matrix entries. Our suggested system has a vast key space and is more effective because of the use of a recursive matrix. As a result, it minimizes the complexity of both time and space. Additionally, it is secure and robust since it is based on the challenging number theory issue known as the elliptic curve-discrete logarithm issue. Received: July 4, 2023Revised: September 15, 2023Accepted: September 26, 2023","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"276 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262582","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}
This work is about symmetric numerical semigroups. The symmetric numerical semigroups are very important in semigroup theory. They play an important role especially in algebraic geometry, coding theory and other areas of algebra. Here, we examine Arf closure of $S_q$ symmetric numerical semigroup, and give some relations between $S_q$ and Arf closure $S_q$ such that $S_q=langle p, p q+krangle$, where $p$ is a prime number and $q geq 1, q in mathbb{Z}$ for $k=1,2$ and $p-1$. Received: June 15, 2023Revised: August 1, 2023Accepted: September 12, 2023
这项工作是关于对称数值半群的。对称数值半群在半群理论中占有非常重要的地位。它们在代数几何、编码理论和其他代数领域发挥着重要作用。本文研究了$S_q$对称数值半群的Arf闭包，并给出了$S_q$与Arf闭包$S_q$之间的一些关系，使得$S_q=langle p, p q+krangle$，其中$p$是质数，$q geq 1, q in mathbb{Z}$对于$k=1,2$和$p-1$。收稿日期:2023年6月15日修稿日期:2023年8月1日收稿日期:2023年9月12日
{"title":"ON ARF CLOSURE OF SOME SYMMETRIC NUMERICAL SEMIGROUPS WITH MULTIPLICITY -PRIME","authors":"Ahmet Çelik","doi":"10.17654/0972555523024","DOIUrl":"https://doi.org/10.17654/0972555523024","url":null,"abstract":"This work is about symmetric numerical semigroups. The symmetric numerical semigroups are very important in semigroup theory. They play an important role especially in algebraic geometry, coding theory and other areas of algebra. Here, we examine Arf closure of $S_q$ symmetric numerical semigroup, and give some relations between $S_q$ and Arf closure $S_q$ such that $S_q=langle p, p q+krangle$, where $p$ is a prime number and $q geq 1, q in mathbb{Z}$ for $k=1,2$ and $p-1$. Received: June 15, 2023Revised: August 1, 2023Accepted: September 12, 2023","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863889","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}
In this paper, we study a class of commutative nonassociative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a nonzero idempotent, any algebra satisfying such an identity admits a Peirce decomposition. Using this decomposition, we study the derivations and representations of algebras of this class. Received: May 6, 2023Revised: May 30, 2023Accepted: July 4, 2023
{"title":"ON A CLASS OF ALGEBRAS SATISFYING AN IDENTITY OF DEGREE FIVE","authors":"Aly GUIRO, Abdoulaye DEMBEGA, André CONSEIBO","doi":"10.17654/0972555523023","DOIUrl":"https://doi.org/10.17654/0972555523023","url":null,"abstract":"In this paper, we study a class of commutative nonassociative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a nonzero idempotent, any algebra satisfying such an identity admits a Peirce decomposition. Using this decomposition, we study the derivations and representations of algebras of this class. Received: May 6, 2023Revised: May 30, 2023Accepted: July 4, 2023","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136374900","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}
{"title":"SOME STRUCTURAL PROPERTIES OF THE QUANTIZED MATRIX ALGEBRA","authors":"Lina Niu, Rabigul Tuniyaz","doi":"10.17654/0972555523022","DOIUrl":"https://doi.org/10.17654/0972555523022","url":null,"abstract":"","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"79 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79044050","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}
{"title":"ON SOME PROPERTY OF -ADIC FAMILIES OF POTENTIALLY SEMI-STABLE REPRESENTATIONS","authors":"A. Yamagami","doi":"10.17654/0972555523021","DOIUrl":"https://doi.org/10.17654/0972555523021","url":null,"abstract":"","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89084103","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}
{"title":"PARAMETRIZATION OF ALGEBRAIC POINTS OF A FAMILY OF ARNTHJENSEN-FLYNN HYPERELLIPTIC CURVES OF A GIVEN DEGREE","authors":"Mohamadou Mor Diogou Diallo, Moussa Fall","doi":"10.17654/0972555523020","DOIUrl":"https://doi.org/10.17654/0972555523020","url":null,"abstract":"","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80316027","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}
{"title":"ORDER THEORY IN STRIP FOLDING","authors":"Yiyang Jia, J. Mitani","doi":"10.17654/0972555523019","DOIUrl":"https://doi.org/10.17654/0972555523019","url":null,"abstract":"","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"117 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73192283","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}
{"title":"TOPOLOGICALLY NOETHERIAN BANACH ALGEBRAS","authors":"M. Mabrouk, E. Saeed","doi":"10.17654/0972555523018","DOIUrl":"https://doi.org/10.17654/0972555523018","url":null,"abstract":"","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"106 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76872105","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：