Cyclotomic cosets and primitive idempotents in semisimple ring

2019 ◽  
Vol 47 (9) ◽  
pp. 3765-3780
Author(s):  
Pinki Devi ◽  
Pankaj Kumar
Keyword(s):  
Cyclotomic Cosets ◽  
Primitive Idempotents ◽  
Semisimple Ring

λ-Mapping and Primitive Idempotents in Semisimple Ring ℜm

2013 ◽  
Vol 41 (10) ◽  
pp. 3679-3694 ◽  
Author(s):  
Pankaj Kumar ◽  
S. K. Arora
Keyword(s):  
Primitive Idempotents ◽  
Semisimple Ring

Semisimplicity of Free Centred Extensions

1995 ◽  
Vol 38 (1) ◽  
pp. 55-58 ◽  
Author(s):  
Miguel Ferrero
Keyword(s):  
Extended Centroid ◽  
Semisimple Ring

AbstractWe prove that a free centred extension R[E] is a semisimple ring if R is a semisimple ring and C[E] is semisimple for every field C which is the extended centroid of a primitive factor of R.

scholarly journals On cyclotomic cosets and code constructions

2016 ◽  
Vol 488 ◽  
pp. 302-319 ◽  
Author(s):  
Giuliano G. La Guardia ◽  
Marcelo M.S. Alves
Keyword(s):  
Cyclotomic Cosets ◽  
Code Constructions

Isomorphism classes of commutative algebras generated by idempotents

2019 ◽  
pp. 2150008
Author(s):  
Kazuyo Inoue ◽  
Hideyasu Kawai ◽  
Nobuharu Onoda
Keyword(s):  
Nonnegative Integer ◽  
Integral Domain ◽  
Algebra Isomorphism ◽  
Infinite Dimensional ◽  
Isomorphism Classes ◽  
Commutative Algebras ◽  
Primitive Idempotents ◽  
Countably Infinite ◽  
Torsion Free

We study commutative algebras generated by idempotents with particular emphasis on the number of primitive idempotents. Let [Formula: see text] be an integral domain with the field of fractions [Formula: see text] and let [Formula: see text] be an [Formula: see text]-algebra which is torsion-free as an [Formula: see text]-module. We show that if [Formula: see text] satisfies the three conditions: [Formula: see text] is generated by idempotents over [Formula: see text]; [Formula: see text] is countably infinite dimensional over [Formula: see text]; [Formula: see text] has [Formula: see text] primitive idempotents for a nonnegative integer [Formula: see text], then [Formula: see text] is uniquely determined up to [Formula: see text]-algebra isomorphism. We also consider the case where [Formula: see text] has countably many primitive idempotents.

scholarly journals Primitive Idempotents of Irreducible Cyclic Codes of Length n

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yuqian Lin ◽  
Qin Yue ◽  
Yansheng Wu
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Matrix Method ◽  
Cyclic Codes ◽  
Prime Divisors ◽  
Primitive Idempotents ◽  
Irreducible Cyclic Codes

Let Fq be a finite field with q elements and n a positive integer. In this paper, we use matrix method to give all primitive idempotents of irreducible cyclic codes of length n, whose prime divisors divide q-1.

Ideals in Topological Rings

1964 ◽  
Vol 16 ◽  
pp. 28-45 ◽  
Author(s):  
Bertram Yood
Keyword(s):  
Topological Ring ◽  
Semisimple Ring

We present here an investigation of the theory of one-sided ideals in a topological ring R. One of our aims is to discuss the question of "left" properties versus "right" properties. A problem of this sort is to decide if (a) all the modular maximal right ideals of R are closed if and only if all the modular maximal left ideals of R are closed. It is shown that this is the case if R is a quasi-Q-ring, that is, if R is bicontinuously isomorphic to a dense subring of a Q-ring (for the notion of a Q-ring see (6) or §2). All normed algebras are quasi-Q-rings. Also (a) holds if R is a semisimple ring with dense socle.

Cyclotomy and arithmetic properties of some families in Z[x]/〈xpq − 1〉

2019 ◽  
Vol 13 (04) ◽  
pp. 2050077
Author(s):  
Sonal Jain ◽  
Sudhir Batra
Keyword(s):  
Finite Fields ◽  
Alternate Proof ◽  
Generalized Cyclotomy ◽  
Cyclotomic Cosets ◽  
Arithmetic Properties

Cyclotomic classes of order 2 with respect to a product of two distinct odd primes [Formula: see text] and [Formula: see text] are represented in some specific forms and using these forms an alternate proof of Theorem 3 of [C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl. 4 (1998) 140–166] is given, when [Formula: see text]. Further, it is observed that these classes are related to [Formula: see text]-cyclotomic cosets, where [Formula: see text] and [Formula: see text] such that gcd([Formula: see text]. Finally, arithmetic properties of some families in [Formula: see text] and hence in [Formula: see text] are studied.

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