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Note on Isomorphism Theorems of Hyperrings
Muthusamy Velrajan,Arjunan Asokkumar
International Journal of Mathematics and Mathematical Sciences , 2010, DOI: 10.1155/2010/376985
Abstract: There are different notions of hyperrings (,
Associate, Hyperdomainlike, and Presimplifiable Hyperrings  [PDF]
Agboola Adesina Abdul Akeem,Davvaz Bijan
Journal of Mathematics , 2014, DOI: 10.1155/2014/458603
Abstract: Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented. 1. Introduction The study of strongly associate rings began with Kaplansky in [1] and was further studied in [2–5]. Domainlike rings and their properties were presented by Axtell et al. in [6]. Presimplifiable rings were introduced by Bouvier in the series of papers [7–11] and were later studied in [2–4]. Further properties of associate and presimplifiable rings were recently presented by Ghanem in [12]. The theory of hyperstructures was introduced in 1934 by Marty [13] at the 8th Congress of Scandinavian Mathematicians. Introduction of the theory has caught the attention and interest of many mathematicians and the theory is now spreading like wild fire. The notion of canonical hypergroups was introduced by Mittas [14]. Some further contributions to the theory can be found in [15–19]. Hyperrings are essentially rings with approximately modified axioms. Hyperrings are of different types introduced by different researchers. Krasner [20] introduced a type of hyperring where + is a hyperoperation and is an ordinary binary operation. Such a hyperring is called a Krasner hyperring. Rota in [21] introduced a type of hyperring where + is an ordinary binary operation and is a hyperoperation. Such a hyperring is called a multiplicative hyperring. de Salvo [22] introduced and studied a type of hyperring where + and are hyperoperations. The most comprehensive reference for hyperrings is Davvaz and Leoreanu-Fotea’s book [18]. Some other references are [23–31]. In this paper, we present and study associate, hyperdomainlike, and presimplifiable hyperrings. The relationships between these new hyperrings are presented. 2. Preliminaries In this section, we will provide some definitions that will be used in the sequel. For full details about associate, domainlike, and presimplifiable rings, the reader should see [1, 4–6, 12]. Also, for details about hyperstructures and hyperrings, the reader should see [12]. Definition 1. Let be a commutative ring with unity. (1) is called an associate ring if whenever any two elements generate the same principal ideal of , there is a unit such that .(2) is called a domainlike ring if all zero divisors of are nilpotent.(3) is called a presimplifiable ring if, for any two elements with , we have or .(4) is called a superassociate ring if
Algebraic Geometry Over Hyperrings  [PDF]
Jaiung Jun
Mathematics , 2015,
Abstract: We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two parts; algebraic aspects and geometric aspects of hyperrings. We first investigate several technical algebraic properties of a hyperring. In the second part, we begin by giving another interpretation of a tropical variety as an algebraic set over the hyperfield which canonically arises from a totally ordered semifield. Then we define a notion of an integral hyperring scheme $(X,\mathcal{O}_X)$ and prove that $\Gamma(X,\mathcal{O}_X)\simeq R$ for any integral affine hyperring scheme $X=Spec R$.
用同??孔法?理孔?事故的方法  [PDF]
王智德
地质与勘探 , 1957,
Abstract: 在?理孔????具事故?,往往最后剩下一段不太?的粗??具,因???的更?,不易把它取上。??一般?理方法是用起重?起拔,或用切管器切?,甚至用??消?。?些方法下?要化?很???,付出很大?力??,而且有?还不可靠。?用同??孔法,?可以大大减??力??,?短?理??,降低成本,?且很可靠。同??孔一般??“半拉爪”?孔,是?理???具事故的方法之一。?事故?具?度不超?0.7公尺,?孔?的地层?6?以下岩石,不管用合金或?粒??的孔都可?。如果故障?具很?,已被切割器切成??仍不能取上,也可用此方法??一?取出一
A class of hyperrings and hyperfields
Marc Krasner
International Journal of Mathematics and Mathematical Sciences , 1983, DOI: 10.1155/s0161171283000265
Abstract: Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H. When the non-zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author [1] as an important technical tool in his theory of approximation of complete valued fields by sequences of such fields. Tne non-commutative theory of hyperrings (particularly Artinian) has been studied in depth by Stratigopoulos [2].
On Subgraph Isomorphism  [PDF]
Sergey Gubin
Computer Science , 2008,
Abstract: Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
原图纸糊布方法  [PDF]
朱明银
地质与勘探 , 1960,
Abstract: 生产矿山为建立一套精确而耐用的地测原图,大都采用原图纸糊布的方法来减小图纸收缩和延长图纸使用寿命。但多数是采用桃胶、亚麻布进行糊制,糊
马铃薯淀粉糊在超声场中凝胶质构特性的变化研究  [PDF]
林静韵,李琳,李坚斌,陈玲,李冰,李晓玺
食品科学 , 2007,
Abstract: ?淀粉糊凝胶特性对食品加工过程有重要指导作用。本实验以马铃薯淀粉糊为研究对象,考察在超声场中,不同超声场条件、不同马铃薯淀粉糊浓度下,马铃薯淀粉凝胶强度的变化规律。结果表明:超声场中马铃薯淀粉凝胶质构分析性质(tpa性质)显著改变,延长超声场作用时间和增加声强会降低凝胶的硬度值、脆度值、粘性值、胶粘性值和耐咀性值。随着马铃薯淀粉糊浓度增大,超声场中马铃薯淀粉糊凝胶的硬度值、胶粘性值和耐咀性值下降趋势变小。
南盘江盆地中三叠统复理石中的同沉积挤压构造――一类新的沉积构造的归类、命名和构造意义探讨  [PDF]
地质论评 , 2003,
Abstract: 南盘江盆地在中三叠世时接受了厚达5000m的复理石沉积,而该复理石中保存有丰富的原生沉积构造。笔者等在这些沉积构造中识别并命名了一类新的构造――同沉积挤压构造,并用简单的实验定性地模拟了该类构造的形成机理。这些同沉积挤压构造包括:挤压皱纹、挤压岩枕、挤压裂隙和挤压皱脊,发育于复理石砂岩层的底面或泥岩层的顶面,是相关砂层或泥层沉积后到成岩前复理石盆地遭受挤压收缩的动态记录。根据这些同沉积挤压构造的方向初步判断,南盘江盆地在中三叠世接受复理石沉积的同时受到了SSW―NNE方向的挤压作用,盆地处于挤压收缩阶段。这些构造为复理石盆地的动态演化研究提供了新的证据。
超声波处理对菱角淀粉糊凝胶质构特性的影响  [PDF]
明建,邓科,谭静
食品科学 , 2009,
Abstract: ?以四川西昌产两角菱角淀粉为原料,利用ta-xt2i物性测定仪,研究超声作用下两角菱角淀粉糊凝胶质构特性的变化。结果表明:在不同超声波作用条件下,不同浓度的两角菱角淀粉糊所形成的凝胶质构特性显著改变,延长超声波作用时间和增加超声强度,会降低凝胶的硬度、咀嚼性、胶着性、弹性、黏聚性以及回复性,并且随着两角菱角淀粉糊浓度的增大,其所形成凝胶的质构特性下降趋势减缓。
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