Relevant bibliographies by topics / Division rings and semisimple Artin rings

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Division rings and semisimple Artin rings'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Division rings and semisimple Artin rings"

1

Simson, Daniel. "On right pure semisimple hereditary rings and an Artin problem." Journal of Pure and Applied Algebra 104, no. 3 (November 1995): 313–32. http://dx.doi.org/10.1016/0022-4049(94)00068-x.

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2

Susanto, Hery, Santi Irawati, Indriati Nurul Hidayah, and Irawati -. "Isomorphism between Endomorphism Rings of Modules over A Semisimple Ring." Journal of the Indonesian Mathematical Society 26, no. 2 (July 10, 2020): 170–74. http://dx.doi.org/10.22342/jims.26.2.824.170-174.

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Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.
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3

García, José L. "Small potential counterexamples to the pure semisimplicity conjecture." Journal of Algebra and Its Applications 17, no. 10 (October 2018): 1850183. http://dx.doi.org/10.1142/s0219498818501839.

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The pure semisimplicity conjecture or pssc states that every left pure semisimple ring has finite representation type. Let [Formula: see text] be division rings, and assume we identify conditions on a [Formula: see text]-[Formula: see text]-bimodule [Formula: see text] which are sufficient to make the triangular matrix ring [Formula: see text] into a left pure semisimple ring which is not of finite representation type. It is then said that those conditions yield a potential counterexample to the pssc. Simson [17–20] gave several such conditions in terms of the sequence of the left dimensions of the left dual bimodules of [Formula: see text]. In this paper, conditions with the same purpose are given in terms of the continued fraction attached to [Formula: see text], and also through arithmetical properties of a division ring extension [Formula: see text].
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Dissertations / Theses on the topic "Division rings and semisimple Artin rings"

1

Pandian, Ravi Samuel. "The structure of semisimple Artinian rings." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/2977.

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Proves two famous theorems attributed to J.H.M. Wedderburn, which concern the structure of noncommutative rings. The two theorems include, (1) how any semisimple Artinian ring is the direct sum of a finite number of simple rings; and, (2) the Wedderburn-Artin Theorem. Proofs in this paper follow those outlined in I.N. Herstein's monograph Noncommutative Rings with examples and details provided by the author.
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2

Procházková, Zuzana. "Význačné prvky grupových okruhů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448402.

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Title: Distinguished elements of group rings Author: Bc. Zuzana Procházková Department: Department of Algebra Supervisor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D., Department of Algebra Abstract: This thesis is about finding idempotents in a group ring. We describe three techniques of finding idempotents in a semisimple group ring and in the last chapter there is an attempt to find idempotents in a group ring that does not have to be semisimple. The first technique uses representations and characters of a group. The second technique finds idempotents through the use of Shoda pairs. The third technique lifts idempotent from the factor ring with the help of CNC system of ideals, which is a generalization of a well-known technique with nilpotent ideals, and it is here extended to group rings formed by non-abelian group and noncommutative ring. iii
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Books on the topic "Division rings and semisimple Artin rings"

1

Brauer groups, Tamagawa measures, and rational points on algebraic varieties. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Division rings and semisimple Artin rings"

1

Rowen, Louis. "Semisimple modules and rings and the Wedderburn-Artin theorem." In Graduate Studies in Mathematics, 33–44. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/091/03.

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