Residue class algebras of enveloping algebras

1973 ◽  
pp. 48-87
Author(s):  
Walter Borho ◽  
Peter Gabriel ◽  
Rudolf Rentschler
Keyword(s):  
Residue Class ◽  
Enveloping Algebras

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

scholarly journals On S-Evolution Algebras and Their Enveloping Algebras

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1195
Author(s):  
Farrukh Mukhamedov ◽  
Izzat Qaralleh
Keyword(s):  
Enveloping Algebras

In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions.

scholarly journals Fox-type problems in enveloping algebras

2008 ◽  
Vol 319 (6) ◽  
pp. 2489-2495 ◽  
Author(s):  
Hamid Usefi
Keyword(s):  
Enveloping Algebras
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