{"title":"Infinite Matrices and Cesàro Sequence Spaces of Non-absolute Type","authors":"F. Başar","doi":"10.5036/MJIU.31.1","DOIUrl":"https://doi.org/10.5036/MJIU.31.1","url":null,"abstract":"In the present paper we essentially deal with to determine the neccessary and sufficient conditions in order for a matrix A=(ank) to belong to the classes (Xp:bs), (Xp:fs), (X1:lp), (Xp:X1) and (lp:X1), respectively. Furthermore, we give the sufficient conditions on a matrix A=(ank) in the class (Xp:lp) for 1<p<∞ and prove a Steinhaus type theorem concerning the disjointness of the classes (Xp:fs)r and (bs:fs). Those sequence spaces are described, below.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"23 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86253001","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 Reductions of Finitely Generated Ideals in Integral Domains","authors":"S. Oda","doi":"10.5036/MJIU.30.21","DOIUrl":"https://doi.org/10.5036/MJIU.30.21","url":null,"abstract":"√(f1,...,fd+1)R[X] [3,p.124]. The question is whether an ideal (f1,...,fd+1) R[X] can be chosen as a reduction of I. We only know the following case of affine domains, which was developed by G. Lyubeznik [4]: Let R be an n-dimensional affine domain over an infinite field k and let I be an ideal of R. Then I has a reduction generated by n+1 elements. He also posed the following conjecture: Let A be a Noetherian ring of dimension n -1 such that the residue field of every maximal ideal of A is infinite. Let I be an ideal of A or A[X] (a polynomial ring. Then I has a reduction generated by n elements. Our objective of this paper is to prove Lyubeznik's conjecture for a Noetherian domain containing an algebraically closed field: Let A be a Noetherian domain containing an algebraically closed field k and let I be an ideal of a polynomial ring A[X] such that I contains a monic","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"94 1","pages":"21-32"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91053072","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":"Note on overrings without a specified element","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.30.9","DOIUrl":"https://doi.org/10.5036/MJIU.30.9","url":null,"abstract":"Anderson-Dobbs-Huckaba ([ADH]) showed that, if each s-overring of D is a PVD, then each overring of D is seminormal. Also they state that the converse does not hold ([ADH, Remark 3.3]). They constructed a domain D such that each overring of D is seminormal, and has an s-overring which is not a PVD. But it does not seem that they constructed an s-overring T of D concretely which is not a PVD. In this paper, we will answer to these Questions. Further, we will give more definite conditions when D or S is integrally closed or 1-dimensional or Noetherian. Next, we will supplement [ADH, Example 3.2] to give a domain D and an s-overring T of D such that each overring of D is seminormal, and T is not a PVD. We note that [ADH] holds for any g-monoid S ([KM], [MK1] and [MK2]). If, for each maximal ideal M of D, the integral closure of DM is a valuation ring, then D is called an i-domain ([P]). The integral closure of D is denoted by D', and the integral closure of S is denoted by S'. If S' is a valuation seinigroup, then S is called an i-seinigroup. The following is a semigroup version of [ADH, Proposition 3.1].","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"26 1","pages":"9-14"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80278791","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 remarks on Krull's conjecture regarding almost integral elements","authors":"Habte Gebru","doi":"10.5036/MJIU.30.15","DOIUrl":"https://doi.org/10.5036/MJIU.30.15","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"70 1","pages":"15-20"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89980154","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":"A Certain Subclass of Meromorphically Convex Functions with Negative Coefficients","authors":"H. Srivastava, H. M. Hossen, M. Aouf","doi":"10.5036/MJIU.30.33","DOIUrl":"https://doi.org/10.5036/MJIU.30.33","url":null,"abstract":"In this paper we obtain coefficient inequalities, and distortion and closure theorems, for the class Λk(α, β, A, B) of meromorphically convex functions with negative coefficients, which we introduce here. We also obtain the class-preserving integral operator of the form:F(z)=c∫10ucf(uz)du (c>0)for the class Λk(α, β, A, B). Conversely, when the image function F(z)∈ Λk(α, β, A, B), we find the radius of convexity of the original function f(z). Several interesting results involving the modified Hadamard product of functions belonging to the class Λk(α, β, A, B) are also derived.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"11 1","pages":"33-51"},"PeriodicalIF":0.0,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81097133","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 Properties between Rings and Semigroups","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.29.9","DOIUrl":"https://doi.org/10.5036/MJIU.29.9","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"83 1","pages":"9-23"},"PeriodicalIF":0.0,"publicationDate":"1997-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86550266","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":"Abstract Treatment of Integration","authors":"Y. Kubota","doi":"10.5036/MJIU.29.41","DOIUrl":"https://doi.org/10.5036/MJIU.29.41","url":null,"abstract":"This is a try to give axiomatic approaches to some integration theories of Perron type and Lusin type for real-valued functions defined on compact intervals in R.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"7 1","pages":"41-54"},"PeriodicalIF":0.0,"publicationDate":"1997-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79040762","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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