Pub Date : 2023-02-01DOI: 10.52547/cgasa.2023.103143
F. Farzalipour, P. Ghiasvand
{"title":"Classification of 1-absorbing comultiplication modules over a pullback ring","authors":"F. Farzalipour, P. Ghiasvand","doi":"10.52547/cgasa.2023.103143","DOIUrl":"https://doi.org/10.52547/cgasa.2023.103143","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46145170","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2023.103288
Francis Woumfo, Etienne Romuald Temgoua, C. Lélé
{"title":"The prime state ideal theorem in state residuated lattices","authors":"Francis Woumfo, Etienne Romuald Temgoua, C. Lélé","doi":"10.52547/cgasa.2023.103288","DOIUrl":"https://doi.org/10.52547/cgasa.2023.103288","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44755460","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2023.103121
M. Aaly Kologani
{"title":"On (semi)topology L-algebras","authors":"M. Aaly Kologani","doi":"10.52547/cgasa.2023.103121","DOIUrl":"https://doi.org/10.52547/cgasa.2023.103121","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45175650","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2022.102914
Xianbo Yang, Dexue Zhang
{"title":"Formal balls of Q-categories","authors":"Xianbo Yang, Dexue Zhang","doi":"10.52547/cgasa.2022.102914","DOIUrl":"https://doi.org/10.52547/cgasa.2022.102914","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49003049","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2022.102934
Gaoxun Zhang, W. He
{"title":"On saturated prefilter monads","authors":"Gaoxun Zhang, W. He","doi":"10.52547/cgasa.2022.102934","DOIUrl":"https://doi.org/10.52547/cgasa.2022.102934","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45061890","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2022.103019
Promit Mukherjee, R. Mukherjee, S. Sardar
{"title":"Action graph of a semigroup act & its functorial connection","authors":"Promit Mukherjee, R. Mukherjee, S. Sardar","doi":"10.52547/cgasa.2022.103019","DOIUrl":"https://doi.org/10.52547/cgasa.2022.103019","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42401633","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2023.103291
{"title":"Persian Abstracts, Vol. 18, No. 1.","authors":"","doi":"10.52547/cgasa.2023.103291","DOIUrl":"https://doi.org/10.52547/cgasa.2023.103291","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44202796","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}
Pub Date : 2023-02-01DOI: 10.52547/cgasa.2023.103290
{"title":"Cover for Vol. 18, No. 1.","authors":"","doi":"10.52547/cgasa.2023.103290","DOIUrl":"https://doi.org/10.52547/cgasa.2023.103290","url":null,"abstract":"","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41934623","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}
Pub Date : 2022-07-01DOI: 10.52547/cgasa.2022.102640
Harshita Tiwari, R. Srivastava
. In this paper, motivated by Cagliari and Mantovani, we have obtained a characterization of injective objects (with respect to the class of embeddings in the category 𝑄 - TOP of 𝑄 -topological spaces) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) , when ( 𝑌, 𝜎 ) is a stratified 𝑄 -topological space, with the help of their 𝑇 0 -reflection. Further, we have proved that for any 𝑄 -topological space ( 𝑌, 𝜎 ) , the existence of an injective hull of (( 𝑋, 𝜏 ) , 𝑓 ) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) is equivalent to the existence of an injective hull of its 𝑇 0 -reflection (( ˜ 𝑋, ˜ 𝜏 ) , ˜ 𝑓 ) in the comma category 𝑄 - TOP /( ˜ 𝑌, ˜ 𝜎 ) (and in the comma category 𝑄 - TOP 0 /( ˜ 𝑌, ˜ 𝜎 ) , where 𝑄 - TOP 0 denotes the category of 𝑇 0 - 𝑄 -topological spaces).
． 本文在Cagliari和Mantovani的激励下，利用它们的𝑇0反射，我们获得了逗号类别𝑄- TOP /(𝑌，)中(𝑌，)是分层的𝑄-拓扑空间时的射射对象(关于𝑄-拓扑空间的𝑄- TOP类别中的嵌入类)的表征。进一步,我们已经证明对任何𝑄拓扑空间(𝑌𝜎)的存在的单射船体((𝑓𝑋𝜏))在逗号类别𝑄-前/(𝑌𝜎)相当于一个单射的存在船体的𝑇0反射((˜𝑋,˜𝜏),˜𝑓)逗号类𝑄-前/(˜𝑌,˜𝜎)(和逗号类别𝑄- 0 /(˜𝑌,˜𝜎),在𝑄-前表示一类𝑇0𝑄拓扑空间)。
{"title":"On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)","authors":"Harshita Tiwari, R. Srivastava","doi":"10.52547/cgasa.2022.102640","DOIUrl":"https://doi.org/10.52547/cgasa.2022.102640","url":null,"abstract":". In this paper, motivated by Cagliari and Mantovani, we have obtained a characterization of injective objects (with respect to the class of embeddings in the category 𝑄 - TOP of 𝑄 -topological spaces) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) , when ( 𝑌, 𝜎 ) is a stratified 𝑄 -topological space, with the help of their 𝑇 0 -reflection. Further, we have proved that for any 𝑄 -topological space ( 𝑌, 𝜎 ) , the existence of an injective hull of (( 𝑋, 𝜏 ) , 𝑓 ) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) is equivalent to the existence of an injective hull of its 𝑇 0 -reflection (( ˜ 𝑋, ˜ 𝜏 ) , ˜ 𝑓 ) in the comma category 𝑄 - TOP /( ˜ 𝑌, ˜ 𝜎 ) (and in the comma category 𝑄 - TOP 0 /( ˜ 𝑌, ˜ 𝜎 ) , where 𝑄 - TOP 0 denotes the category of 𝑇 0 - 𝑄 -topological spaces).","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48547457","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}
Pub Date : 2022-07-01DOI: 10.52547/cgasa.2022.102622
Z. Keshtkar, R. Mohamadian, M. Namdari, M. Zeinali
. In this article we consider some relations between the topological properties of the spaces 𝑋 and 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) with algebraic properties of 𝐶 𝑐 ( 𝑋 ) . We observe that the compactness of 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is equivalent to the von-Neumann regularity of 𝑞 𝑐 ( 𝑋 ) , the classical ring of quotients of 𝐶 𝑐 ( 𝑋 ) . Furthermore, we show that if 𝑋 is a strongly zero-dimensional space, then each contraction of a minimal prime ideal of 𝐶 ( 𝑋 ) is a minimal prime ideal of 𝐶 𝑐 ( 𝑋 ) and in this case 𝑀𝑖𝑛 ( 𝐶 ( 𝑋 )) and 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) are homeomorphic spaces. We also observe that if 𝑋 is an 𝐹 𝑐 -space, then 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is compact if and only if 𝑋 is countably basically disconnected if and only if 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is homeomorphic with 𝛽 0 𝑋 . Finally, by introducing 𝑧 ◦ 𝑐 -ideals, countably cozero complemented spaces, we obtain some conditions on 𝑋 for which 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) becomes compact, basically disconnected and extremally disconnected.
{"title":"On some properties of the space of minimal prime ideals of 𝐶𝑐 (𝑋)","authors":"Z. Keshtkar, R. Mohamadian, M. Namdari, M. Zeinali","doi":"10.52547/cgasa.2022.102622","DOIUrl":"https://doi.org/10.52547/cgasa.2022.102622","url":null,"abstract":". In this article we consider some relations between the topological properties of the spaces 𝑋 and 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) with algebraic properties of 𝐶 𝑐 ( 𝑋 ) . We observe that the compactness of 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is equivalent to the von-Neumann regularity of 𝑞 𝑐 ( 𝑋 ) , the classical ring of quotients of 𝐶 𝑐 ( 𝑋 ) . Furthermore, we show that if 𝑋 is a strongly zero-dimensional space, then each contraction of a minimal prime ideal of 𝐶 ( 𝑋 ) is a minimal prime ideal of 𝐶 𝑐 ( 𝑋 ) and in this case 𝑀𝑖𝑛 ( 𝐶 ( 𝑋 )) and 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) are homeomorphic spaces. We also observe that if 𝑋 is an 𝐹 𝑐 -space, then 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is compact if and only if 𝑋 is countably basically disconnected if and only if 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) is homeomorphic with 𝛽 0 𝑋 . Finally, by introducing 𝑧 ◦ 𝑐 -ideals, countably cozero complemented spaces, we obtain some conditions on 𝑋 for which 𝑀𝑖𝑛 ( 𝐶 𝑐 ( 𝑋 )) becomes compact, basically disconnected and extremally disconnected.","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44838581","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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