{"title":"Inductive groupoids and normal categories of regular semigroups","authors":"A. R. Rajan","doi":"10.1515/9783110542400-016","DOIUrl":"https://doi.org/10.1515/9783110542400-016","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80825327","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":"Separability in algebra and category theory","authors":"R. Wisbauer","doi":"10.1515/9783110542400-022","DOIUrl":"https://doi.org/10.1515/9783110542400-022","url":null,"abstract":"Separable field extensions are essentially known since the 19th century and their formal definition was given by Ernst Steinitz in 1910. In this survey we first recall this notion and equivalent characterisations. Then we outline how these were extended to more general structures, leading to separable algebras (over rings), Frobenius algebras, (non associative) Azumaya algebras, coalgebras, Hopf algebras, and eventually to separable functors. The purpose of the talk is to demonstrate that the development of new notions and definitions can lead to simpler formulations and to a deeper understanding of the original concepts. The formalism also applies to algebras and coalgebras over semirings and S-acts (transition systems).","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80481464","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 note on cess-lattices","authors":"S. Nimbhorkar, Deepali Brijlal Banswal","doi":"10.1515/9783110542400-013","DOIUrl":"https://doi.org/10.1515/9783110542400-013","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86741141","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":"Additive central m-power skew-commuting maps on semiprime rings","authors":"Tsiu-Kwen Lee","doi":"10.1515/9783110542400-012","DOIUrl":"https://doi.org/10.1515/9783110542400-012","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87457015","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":"Projective ideals of differential polynomial rings over hnp rings","authors":"H. Marubayashi, A. Ueda","doi":"10.1515/9783110542400-011","DOIUrl":"https://doi.org/10.1515/9783110542400-011","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"279 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73655363","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 construction of global actions for partial actions","authors":"Sharma Ram Parkash, Meenakshi Ram Parkash","doi":"10.1515/9783110542400-020","DOIUrl":"https://doi.org/10.1515/9783110542400-020","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76718657","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":"Properties inherited by direct sums of copies of a module","authors":"J. Park, S. Rizvi","doi":"10.1515/9783110542400-014","DOIUrl":"https://doi.org/10.1515/9783110542400-014","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84379585","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":"Generalized skew derivations satisfying the second posner’s theorem on lie ideals","authors":"L. Carini, V. Filippis","doi":"10.1515/9783110542400-006","DOIUrl":"https://doi.org/10.1515/9783110542400-006","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79833804","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 new fixed point results in b-metric spaces","authors":"I. Yildirim, A. H. Ansari","doi":"10.1515/taa-2018-0009","DOIUrl":"https://doi.org/10.1515/taa-2018-0009","url":null,"abstract":"Abstract In this paper, we consider, discuss, improve and generalize recent fixed point results for mappings in b-metric space. These results are generalizations of the analogous ones recently proved by Khojasteh et al. [12] and Demma et al. [8].","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"6 1","pages":"102 - 106"},"PeriodicalIF":0.0,"publicationDate":"2018-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2018-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42213215","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 locally compact shift-continuous topologies on the α-bicyclic monoid","authors":"S. Bardyla","doi":"10.1515/taa-2018-0003","DOIUrl":"https://doi.org/10.1515/taa-2018-0003","url":null,"abstract":"Abstract A topology τ on a monoid S is called shift-continuous if for every a, b ∈ S the two-sided shift S → S, x ↦ axb, is continuous. For every ordinal α ≤ ω, we describe all shift-continuous locally compact Hausdorff topologies on the α-bicyclic monoid Bα. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies on Bα is anti-isomorphic to the segment of [1, α] of ordinals, endowed with the natural well-order. Also we prove that for each ordinal α the α + 1-bicyclic monoid Bα+1 is isomorphic to the Bruck extension of the α-bicyclic monoid Bα.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"6 1","pages":"34 - 42"},"PeriodicalIF":0.0,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2018-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47899006","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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