scholarly journals Determining the Noetherian Property of Generalized Power Series Modules by Using X-Sub-Exact Sequence

2021 ◽  
Vol 1751 ◽  
pp. 012028
Author(s):  
A Faisol ◽  
Ftriani ◽  
Sifriyani
Keyword(s):  
Power Series ◽  
Exact Sequence ◽  
Generalized Power Series ◽  
Noetherian Property

scholarly journals The X[[S]]-Sub-Exact Sequence of Generalized Power Series Rings

2020 ◽  
Vol 11 (2) ◽  
pp. 299-306
Author(s):  
Wesly Agustinus Pardede ◽  
Ahmad Faisol ◽  
Fitriani Fitriani
Keyword(s):  
Power Series ◽  
Exact Sequence ◽  
Generalized Power Series ◽  
Ordered Monoid ◽  
Power Series Rings

Let  be a ring,  a strictly ordered monoid, and K, L, M are R-modules. Then, we can construct the Generalized Power Series Modules (GPSM) K[[S]], L[[S]], and M[[S]], which are the module over the Generalized Power Series Rings (GPSR) R[[S]]. In this paper, we investigate the property of X[[S]]-sub-exact sequence on GPSM L[[S]] over GPSR R[[S]].  

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

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