{"title":"APPENDIX","authors":"","doi":"10.1142/9789811219986_0010","DOIUrl":"https://doi.org/10.1142/9789811219986_0010","url":null,"abstract":"","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114836357","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":"RATIONAL AND REAL NUMBERS","authors":"Julius Wihelm Richard, Dedekind","doi":"10.1142/9789811219986_0004","DOIUrl":"https://doi.org/10.1142/9789811219986_0004","url":null,"abstract":"• What other properties do the Rational Numbers have that characterize them? Rational Order Is (Q,+,•) an ordered integral domain? Recall the definition of ordered. Ordered Integral Domain: Contains a subset D+ with the following properties. 1. If a, b ∈ D+ ,then a + b ∈ D+ (closure) 2. If a , b ∈ D+ , then a • b ∈ D+ (closure) 3. For each a ∈ Integral Domain D exactly one of these holds a = 0, a ∈ D+, -a ∈ D+ (Trichotomy)","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131453283","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":"ALGEBRAIC STRUCTURES - AN OVERVIEW","authors":"","doi":"10.1142/9789811219986_0006","DOIUrl":"https://doi.org/10.1142/9789811219986_0006","url":null,"abstract":"","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128609124","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":"RINGS AND FIELDS","authors":"Sergei Silvestrov","doi":"10.1007/978-1-84628-181-5_1","DOIUrl":"https://doi.org/10.1007/978-1-84628-181-5_1","url":null,"abstract":"","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130116726","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":"GROUPS","authors":"Steven J. Rosenberg","doi":"10.1002/9781119111771.app2","DOIUrl":"https://doi.org/10.1002/9781119111771.app2","url":null,"abstract":"The group is the basic algebraic structure with one operation. Groups appear in many contexts in this book. For example, all the signal domains introduced in Chapters 2–5 have the structure of an additive commutative group. Also, sets of transformations of domains and signals have the structure of a noncommutative group. This is used extensively in Chapter 12. This appendix provides basic definitions and properties of groups, but any standard text on abstract algebra should be consulted for a more detailed treatment, e.g, part I of Dummit and Foote (2004) or chapter 1 of Miller (1972).","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123423346","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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