Special Issue III最新文献

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Impact of Language Teaching Approach in Sanskrit and Language as English 语言教学方法对梵语和英语的影响
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp233-235
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引用次数: 0
Surface Characteristic’s Techniques 表面特性技术
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp249-251
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引用次数: 0
Laser and Their Applications 激光及其应用
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp188-193
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引用次数: 0
Spread and Preventions of COVID-19: A Review COVID-19的传播与预防:综述
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp279-282
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引用次数: 0
Design and Creation a Bungalow by Using Autocad Software 用Autocad软件设计制作一座平房
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp76-82
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引用次数: 0
Diagnosis of CTS and non-CTS Sufferers Using Surface Electromyography Signals 表面肌电信号诊断CTS和非CTS患者
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp144-146
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引用次数: 0
A Study on Algebra of Groups and Rings Structures in Mathematics 数学中群与环结构的代数研究
Special Issue III Pub Date : 1900-01-01 DOI: 10.20431/2347-3142.0501004
Vijayashree S. Gaonkar
{"title":"A Study on Algebra of Groups and Rings Structures in Mathematics","authors":"Vijayashree S. Gaonkar","doi":"10.20431/2347-3142.0501004","DOIUrl":"https://doi.org/10.20431/2347-3142.0501004","url":null,"abstract":"Algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Algebra deals with the more general concept of sets is a collection of all objects (called elements) selected by property specific for the set. All collections of the familiar types of numbers are sets. Set theory is a branch of logic and not technically a branch of algebra. Binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure. Addition (+), subtraction (−), multiplication (×), and division (÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices, vectors, and polynomials. Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a, and is necessarily unique, if it exists. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. Not all sets and operator combinations have an identity element. The inverse of a is written −a, and for multiplication the inverse is written a −1 . A general two-sided inverse element a −1 satisfies the property that a ∗ a −1 = e and a −1 ∗ a = e, where e is the identity element. Associativity is, the grouping of the numbers to be added does not affect the sum is (2 + 3) + 4 = 2 + (3 + 4). Commutative is, the order of the numbers does not affect the result is 2 + 3 = 3 + 2. Combining the concepts gives group and ring one of the most important structures in mathematics. A group is a combination of a set S and a single binary operation is an identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a. A group is also commutative—that is, for any two members a and b of S, a ∗ b is identical to b ∗ a—then the group is said to be abelian. A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not required. The additive (+) identity element is written as 0 and the additive inverse of a is written as −a. Keyword: Groups, Rings and Fields are axiomatically and algebra","PeriodicalId":349092,"journal":{"name":"Special Issue III","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121813977","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: 1
“Automatic Street Light” Using Transistor as a Switch 使用晶体管作为开关的“自动路灯”
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp283-286
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引用次数: 0
Fluorescence Spectroscopy and its Applications in Medical Field: A Review 荧光光谱技术及其在医学领域的应用综述
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp252-262
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引用次数: 0
Fabrication and Testing of E-Glass Epoxy Prosthetic Leg E-Glass环氧树脂假腿的制备与测试
Special Issue III Pub Date : 1900-01-01 DOI: 10.14233/ajomc.2021.ajomc-pp92-94
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引用次数: 0
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