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Relevant bibliographies by topics / Abelian structures

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Journal articles

Academic literature on the topic 'Abelian structures'

Author: Grafiati

Published: 28 September 2024

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Journal articles on the topic "Abelian structures"

1

Lu, Jianwei, та Liguo He. "On the Structures of Abelianπ-Regular Rings". International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/842313.

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Assume thatRis an Abelian ring. In this paper, we characterize the structure ofRwheneverRisπ-regular. It is also proved that an Abelianπ-regular ring is isomorphic to the subdirect sum of some metadivision rings.

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2

Clarke, Francis. "Counting abelian group structures." Proceedings of the American Mathematical Society 134, no. 10 (2006): 2795–99. http://dx.doi.org/10.1090/s0002-9939-06-08396-1.

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CONSOLE, S., A. FINO, and Y. S. POON. "STABILITY OF ABELIAN COMPLEX STRUCTURES." International Journal of Mathematics 17, no. 04 (2006): 401–16. http://dx.doi.org/10.1142/s0129167x06003576.

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Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [7] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension.

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Poon, Yat Sun. "Abelian Complex Structures and Generalizations." Complex Manifolds 8, no. 1 (2021): 247–66. http://dx.doi.org/10.1515/coma-2020-0117.

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Abstract After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such structure and illustrate this new concept with a variety of examples.

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5

Tang, Guoliang. "Abelian model structures on comma categories." Ukrains’kyi Matematychnyi Zhurnal 76, no. 3 (2024): 373–81. http://dx.doi.org/10.3842/umzh.v76i3.7289.

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UDC 512.64 Let A and B be bicomplete Abelian categories, which both have enough projectives and injectives and let T : A → B be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on A and B can be amalgamated into a global hereditary Abelian model structure on the comma category ( T ↓ B ) . As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.

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6

Goswami, Amartya. "Salamander lemma for non-abelian group-like structures." Journal of Algebra and Its Applications 19, no. 02 (2019): 2050022. http://dx.doi.org/10.1142/s021949882050022x.

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It is well known that the classical diagram lemmas of homological algebra for abelian groups can be generalized to non-abelian group-like structures, such as groups, rings, algebras, loops, etc. In this paper, we establish such a generalization of the “salamander lemma” due to G. M. Bergman, in a self-dual axiomatic context (developed originally by Z. Janelidze), which applies to all usual non-abelian group-like structures and also covers axiomatic contexts such as semi-abelian categories in the sense of G. Janelidze, L. Márki and W. Tholen and exact categories in the sense of M. Grandis.

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7

Yu, Chia-Fu. "Abelian varieties over finite fields as basic abelian varieties." Forum Mathematicum 29, no. 2 (2017): 489–500. http://dx.doi.org/10.1515/forum-2014-0141.

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AbstractIn this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic ${p>0}$ is isogenous to another one defined over a finite field. We also show that the category of abelian varieties over finite fields up to isogeny can be embedded into the category of basic abelian varieties with suitable endomorphism structures. Using this connection, we derive a new mass formula for a finite orbit of polarized abelian surfaces over a finite field.

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8

Fokina, E., J. F. Knight, A. Melnikov, S. M. Quinn, and C. Safranski. "Classes of Ulm type and coding rank-homogeneous trees in other structures." Journal of Symbolic Logic 76, no. 3 (2011): 846–69. http://dx.doi.org/10.2178/jsl/1309952523.

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AbstractThe first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelianp-groups, the class of Abelian torsion groups, and the special class of “rank-homogeneous” trees. We consider these conditions as a possible definition of what it means for a class of structures to have “Ulm type”. The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply this result to show that there is no Turing computable embedding of the class of graphs into the class of “rank-homogeneous” trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a “rank-preserving” Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank.

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9

Remm, Elisabeth, and Michel Goze. "Affine structures on abelian Lie groups." Linear Algebra and its Applications 360 (February 2003): 215–30. http://dx.doi.org/10.1016/s0024-3795(02)00452-4.

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10

Yu, Chia-Fu. "Lifting abelian varieties with additional structures." Mathematische Zeitschrift 242, no. 3 (2002): 427–41. http://dx.doi.org/10.1007/s002090100350.

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