Bulletin of the Korean Mathematical Society最新文献

{"title":"REVERSIBLE AND PSEUDO-REVERSIBLE RINGS","authors":"Juan Huang, Hai-Lan Jin, Yang Lee, Zhelin Piao","doi":"10.4134/BKMS.B181038","DOIUrl":"https://doi.org/10.4134/BKMS.B181038","url":null,"abstract":"This article concerns the structure of idempotents in reversible and pseudo-reversible rings in relation with various sorts of ring extensions. It is known that a ring R is reversible if and only if ab ∈ I(R) for a, b ∈ R implies ab = ba; and a ring R shall be said to be pseudoreversible if 0 6= ab ∈ I(R) for a, b ∈ R implies ab = ba, where I(R) is the set of all idempotents in R. Pseudo-reversible is seated between reversible and quasi-reversible. It is proved that the reversibility, pseudoreversibility, and quasi-reversibility are equivalent in Dorroh extensions and direct products. Dorroh extensions are also used to construct several sorts of rings which are necessary in the process. Throughout every ring is an associative ring with identity unless otherwise stated. Let R be a ring. Use I(R), N∗(R), N∗(R), W (R), N(R), and J(R) to denote the set of all idempotents, the upper nilradical (i.e., the sum of all nil ideals), the lower nilradical (i.e., the intersection of all minimal prime ideals), the Wedderburn radical (i.e., the sum of all nilpotent ideals), the set of all nilpotent elements, and the Jacobson radical in R, respectively. Note N∗(R) ⊆ N(R). Write I(R)′ = {e ∈ I(R) | e 6= 0}. Z(R) denotes the center of R. The polynomial (power series) ring with an indeterminate x over R is denoted by R[x] (R[[x]]). Z and Zn denote the ring of integers and the ring of integers modulo n, respectively. Let n ≥ 2. Denote the n by n full (resp., upper triangular) matrix ring over R by Matn(R) (resp., Tn(R)), and Dn(R) = {(aij) ∈ Tn(R) | a11 = · · · = ann}. Use Eij for the matrix with (i, j)entry 1 and zeros elsewhere, and In denotes the identity matrix in Matn(R). Given a set S, |S| means the cardinality of S. We use ∏ to denote the direct product of rings. Following Cohn [2], a ring R (possibly without identity) is called reversible if ab = 0 for a, b ∈ R implies ba = 0. Anderson and Camillo [1] used the term ZC2 for the reversibility. A ring (possibly without identity) is usually said to be reduced if it has no nonzero nilpotent elements. Many commutative Received October 30, 2018; Revised January 17, 2019; Accepted February 7, 2019. 2010 Mathematics Subject Classification. 16U80, 16S50, 16S36.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1257-1272"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70360624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL","authors":"Yonggeun Cho, Misung Lee","doi":"10.4134/BKMS.B190029","DOIUrl":"https://doi.org/10.4134/BKMS.B190029","url":null,"abstract":"We show the existence of ground state and orbital stability of standing waves of nonlinear Schrödinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in H1. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1601-1615"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RIEMANNIAN SUBMANIFOLDS WITH CONCIRCULAR CANONICAL FIELD","authors":"Bang‐Yen Chen, S. Wei","doi":"10.4134/BKMS.B181232","DOIUrl":"https://doi.org/10.4134/BKMS.B181232","url":null,"abstract":"Let M̃ be a Riemannian manifold equipped with a concircular vector field X̃ and M a submanifold (with its induced metric) of M̃ . Denote by X the restriction of X̃ on M and by XT the tangential component of X, called the canonical field of M . In this article we study submanifolds of M̃ whose canonical field XT is also concircular. Several characterizations and classification results in this respect are obtained.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1525-1537"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MINIMAL AND CONSTANT MEAN CURVATURE SURFACES IN 3 FOLIATED BY CIRCLES","authors":"Sung-Ho Park","doi":"10.4134/BKMS.B181266","DOIUrl":"https://doi.org/10.4134/BKMS.B181266","url":null,"abstract":"We classify minimal surfaces in S3 which are foliated by circles and ruled constant mean curvature (cmc) surfaces in S3. First we show that minimal surfaces in S3 which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric S1-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in S3 up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in S3 (cf. Theorem 3).","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1539-1550"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GENERATING NON-JUMPING NUMBERS OF HYPERGRAPHS","authors":"Shaoqiang Liu, Yuejian Peng","doi":"10.4134/BKMS.B180808","DOIUrl":"https://doi.org/10.4134/BKMS.B180808","url":null,"abstract":"The concept of jump concerns the distribution of Turán densities. A number α ∈ [0, 1) is a jump for r if there exists a constant c > 0 such that if the Turán density of a family F of r-uniform graphs is greater than α, then the Turán density of F is at least α+c. To determine whether a number is a jump or non-jump has been a challenging problem in extremal hypergraph theory. In this paper, we give a way to generate non-jumps for hypergraphs. We show that if α, β are non-jumps for r1, r2 ≥ 2 respectively, then αβ(r1+r2)!r r1 1 r r2 2 r1!r2!(r1+r2) r1+r2 is a non-jump for r1 + r2. We also apply the Lagrangian method to determine the Turán density of the extension of the (r − 3)-fold enlargement of a 3-uniform matching.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1027-1039"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70360248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SR-ADDITIVE CODES","authors":"Saadoun Mahmoudi, K. Samei","doi":"10.4134/BKMS.B180995","DOIUrl":"https://doi.org/10.4134/BKMS.B180995","url":null,"abstract":"In this paper, we introduce SR-additive codes as a generalization of the classes of ZprZps and Z2Z2[u]-additive codes, where S is an R-algebra and an SR-additive code is an R-submodule of Sα × Rβ . In particular, the definitions of bilinear forms, weight functions and Gray maps on the classes of ZprZps and Z2Z2[u]-additive codes are generalized to SR-additive codes. Also the singleton bound for SR-additive codes and some results on one weight SR-additive codes are given. Among other important results, we obtain the structure of SR-additive cyclic codes. As some results of the theory, the structure of cyclic Z2Z4, ZprZps , Z2Z2[u], (Z2)(Z2+uZ2+uZ2), (Z2+uZ2)(Z2+uZ2+uZ2), (Z2)(Z2+uZ2+vZ2) and (Z2 + uZ2)(Z2 + uZ2 + vZ2)-additive codes are presented.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"34 1 1","pages":"1235-1255"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70360477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SEIBERG-WITTEN-LIKE EQUATIONS ON THE STRICTLY PSEUDOCONVEX CR-3 MANIFOLDS","authors":"S. Eker","doi":"10.4134/BKMS.B181273","DOIUrl":"https://doi.org/10.4134/BKMS.B181273","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1551-1567"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A NOTE ON GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS","authors":"Feng Liu","doi":"10.4134/BKMS.B180053","DOIUrl":"https://doi.org/10.4134/BKMS.B180053","url":null,"abstract":"In the present paper, we establish certain Lp bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class Fβ(S). Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley g∗ λfunctions and area integrals are also presented.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1099-1115"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70358625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rings and modules characterized by opposites of FP-injectivity","authors":"E. Büyükaşık, Gizem Kafkas-Demirci","doi":"10.4134/BKMS.B180325","DOIUrl":"https://doi.org/10.4134/BKMS.B180325","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"439-450"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A NOTE ON THE FIRST ORDER COMMUTATOR C 2","authors":"Wenjuan Li, Suying Liu","doi":"10.4134/BKMS.B180646","DOIUrl":"https://doi.org/10.4134/BKMS.B180646","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"885-898"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}