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Mappings preserving sum of products a∘b+ba∗ on factor von Neumann algebras 保因式冯·诺伊曼代数上a°b+ba *积和的映射
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/ADM1482
J. M. Ferreira, M. Marietto
{"title":"Mappings preserving sum of products a∘b+ba∗ on factor von Neumann algebras","authors":"J. M. Ferreira, M. Marietto","doi":"10.12958/ADM1482","DOIUrl":"https://doi.org/10.12958/ADM1482","url":null,"abstract":"Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping Φ:A→B satisfies Φ(a∘b+ba∗)=Φ(a)∘Φ(b)+Φ(b)Φ(a)∗ (where ∘ is the special Jordan product on A and B, respectively), for all elements a,b∈A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417839","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: 4
Skew PBW extensions over symmetric rings 对称环上的斜PBW扩展
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1767
A. Reyes, H. Suárez
{"title":"Skew PBW extensions over symmetric rings","authors":"A. Reyes, H. Suárez","doi":"10.12958/adm1767","DOIUrl":"https://doi.org/10.12958/adm1767","url":null,"abstract":"Our purpose in this paper is to characterize skew PBW extensions over several weak symmetric rings. As a consequence of our treatment, we extend results in the literature concerning the property of symmetry for commutative rings and skew polynomial rings.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419570","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: 2
On the kernels of higher R-derivations of R[x1,…,xn] 关于R[x1，…，xn]的高R阶导数的核
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1236
S. Kour
{"title":"On the kernels of higher R-derivations of R[x1,…,xn]","authors":"S. Kour","doi":"10.12958/adm1236","DOIUrl":"https://doi.org/10.12958/adm1236","url":null,"abstract":"Let R be an integral domain and A=R [x1, . . . ,xn] be the polynomial ring innvariables. In this article, we studythe kernel of higher R-derivation D of A. It is shown that if R isa HCF ring and tr. degR (AD)⩽1 then AD=R[f] for some f ∈ A.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417146","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: 0
A study on dual square free modules 对偶平方自由模的研究
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1512
M. Medina-Bárcenas, D. Keskin Tütüncü, Y. Kuratomi
{"title":"A study on dual square free modules","authors":"M. Medina-Bárcenas, D. Keskin Tütüncü, Y. Kuratomi","doi":"10.12958/adm1512","DOIUrl":"https://doi.org/10.12958/adm1512","url":null,"abstract":"Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule of Mis fully invariant. Let M=Li∈I Mi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free for all i ∈ I and, Mi and Lj=iMj are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let M be a quasi-projective module. If End R(M) is right dual square free, then M is dual square free. In addition, if M is finitely generated, then End R(M) is right dual square free whene ver M is dual square free. We give several examples illustrating our hypotheses.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66418356","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: 0
Free abelian trioids 自由阿贝尔三样体
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1860
Y. Zhuchok
{"title":"Free abelian trioids","authors":"Y. Zhuchok","doi":"10.12958/adm1860","DOIUrl":"https://doi.org/10.12958/adm1860","url":null,"abstract":"We construct a free abelian trioid and describe the least abelian congruence on a free trioid.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420364","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: 2
F-supplemented modules F补充模块
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2020-12-30 DOI: 10.12958/adm1185
S. Özdemir
{"title":"F-supplemented modules","authors":"S. Özdemir","doi":"10.12958/adm1185","DOIUrl":"https://doi.org/10.12958/adm1185","url":null,"abstract":"Let R be a ring, let M be a left R-module, and let U,V,F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F⊆X⊆M such that U+X=M, or equivalently, F⊆V, U+V=M and U∩V is F-small in V. If every submodule of M has an F-supplement, then we call M an F-supplemented module. In this paper, we introduce and investigate F-supplement submodules and (amply) F-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) F-supplemented modules in terms of their certain submodules.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41977131","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
Spectra of locally matrix algebras 局部矩阵代数的谱
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2020-11-16 DOI: 10.12958/ADM1734
O. Bezushchak
{"title":"Spectra of locally matrix algebras","authors":"O. Bezushchak","doi":"10.12958/ADM1734","DOIUrl":"https://doi.org/10.12958/ADM1734","url":null,"abstract":"We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier–Baranov Theorem. As an application of our description of spectra, we determine embeddings of locally matrix algebras.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45747674","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
Coarse structures on groups defined by conjugations 共轭定义群上的粗结构
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2020-08-03 DOI: 10.12958/adm1737
I. Protasov, K. Protasova
{"title":"Coarse structures on groups defined by conjugations","authors":"I. Protasov, K. Protasova","doi":"10.12958/adm1737","DOIUrl":"https://doi.org/10.12958/adm1737","url":null,"abstract":"For a group G, we denote by G↔ the coarse space on G endowed with the coarse structure with the base {{(x,y)∈G×G:y∈xF}:F∈[G]<ω}, xF={z−1xz:z∈F}. Our goal is to explore interplays between algebraic properties of G and asymptotic properties of G↔. In particular, we show that asdim G↔=0 if and only if G/ZG is locally finite, ZG is the center of G. For an infinite group G, the coarse space of subgroups of G is discrete if and only if G is a Dedekind group.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45264680","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: 0
Approximating length-based invariants in atomic Puiseux monoids 原子Puiseux模群中基于长度的不变量的近似
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2020-07-18 DOI: 10.12958/adm1760
Harold Polo
{"title":"Approximating length-based invariants in atomic Puiseux monoids","authors":"Harold Polo","doi":"10.12958/adm1760","DOIUrl":"https://doi.org/10.12958/adm1760","url":null,"abstract":"A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42436534","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: 0
A virtually 2-step nilpotent group with polynomial geodesic growth 具有多项式测地增长的一个几乎两步幂零群
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2020-07-14 DOI: 10.12958/adm1667
A. Bishop, M. Elder
{"title":"A virtually 2-step nilpotent group with polynomial geodesic growth","authors":"A. Bishop, M. Elder","doi":"10.12958/adm1667","DOIUrl":"https://doi.org/10.12958/adm1667","url":null,"abstract":"A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43413178","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
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