scholarly journals Non-trivial extension of Starobinsky inflation

2021 ◽  
pp. 100822
Author(s):  
Salomeh Khoeini-Moghaddam
Keyword(s):  
Trivial Extension

scholarly journals Jordan centralizer maps on trivial extension algebras

2020 ◽  
Vol 53 (1) ◽  
pp. 58-66
Author(s):  
Mohammad Ali Bahmani ◽  
Fateme Ghomanjani ◽  
Stanford Shateyi
Keyword(s):  
Trivial Extension ◽  
Triangular Algebra ◽  
Trivial Extension Algebra ◽  
Extension Algebra

AbstractThe structure of Jordan centralizer maps is investigated on trivial extension algebras. One may obtain some conditions under which a Jordan centralizer map on a trivial extension algebra is a centralizer map. As an application, we characterize the Jordan centralizer map on a triangular algebra.

ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS

2012 ◽  
Vol 11 (04) ◽  
pp. 1250079 ◽  
Author(s):  
A. ALHEVAZ ◽  
A. MOUSSAVI
Keyword(s):  
Polynomial Rings ◽  
Trivial Extension ◽  
Skew Polynomial Ring ◽  
Matrix Rings ◽  
Skew Polynomial Rings ◽  
Armendariz Rings ◽  
Ore Extensions ◽  
Necessary And Sufficient ◽  
Skew Polynomial ◽  
Armendariz Ring

Let R be a ring with an endomorphism α and α-derivation δ. By [A. R. Nasr-Isfahani and A. Moussavi, Ore extensions of skew Armendariz rings, Comm. Algebra 36(2) (2008) 508–522], a ring R is called a skew Armendariz ring, if for polynomials f(x) = a0 + a1 x + ⋯ + anxn, g(x) = b0+b1x + ⋯ + bmxm in R[x; α, δ], f(x)g(x) = 0 implies a0bj = 0 for each 0 ≤ j ≤ m. In this paper, radicals of the skew polynomial ring R[x; α, δ], in terms of a skew Armendariz ring R, is determined. We prove that several properties transfer between R and R[x; α, δ], in case R is an α-compatible skew Armendariz ring. We also identify some "relatively maximal" skew Armendariz subrings of matrix rings, and obtain a necessary and sufficient condition for a trivial extension to be skew Armendariz. Consequently, new families of non-reduced skew Armendariz rings are presented and several known results related to Armendariz rings and skew polynomial rings will be extended and unified.

scholarly journals Representation-finite trivial extension algebras

1984 ◽  
Vol 33 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Ibrahim Assem ◽  
Dieter Happel ◽  
Oscar Roldán
Keyword(s):  
Trivial Extension

A characterization of a trivial extension which is a Frohenius one

1980 ◽  
Vol 34 (1) ◽  
pp. 111-113 ◽  
Author(s):  
Yoshimi Kitamura
Keyword(s):  
Trivial Extension

Reflexive property on rings with involution

2019 ◽  
Vol 12 (07) ◽  
pp. 2050011
Author(s):  
Arnab Bhattacharjee ◽  
Uday Shankar Chakraborty
Keyword(s):  
Ring Theory ◽  
Trivial Extension ◽  
Noncommutative Ring ◽  
Rings With Involution ◽  
Noncommutative Ring Theory

Mason introduced the notion of reflexive property for rings which play roles in noncommutative ring theory. In this paper, we extend this property to rings with involution and investigate their properties. We provide many examples of these rings and also consider some extensions such as trivial extension, Dorroh extension, etc.

scholarly journals THE FIRST COHOMOLOGY GROUP OF THE TRIVIAL EXTENSION OF A MONOMIAL ALGEBRA

2004 ◽  
Vol 03 (02) ◽  
pp. 143-159 ◽  
Author(s):  
CLAUDE CIBILS ◽  
MARÍA JULIA REDONDO ◽  
MANUEL SAORÍN
Keyword(s):  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Trivial Extension ◽  
Monomial Algebra ◽  
Finite Dimensional ◽  
Hochschild Cohomology Group ◽  
First Cohomology Group

Given a finite-dimensional monomial algebra A, we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH1(A) and Alt (DA) of the first Hochschild cohomology group HH1(TA). From these a formula for the dimension of HH1(TA) can be derived.

scholarly journals Quasi Regular Modules and Trivial Extension

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Chillumuntala JAYARAM ◽  
Ünsal TEKİR ◽  
Suat KOÇ
Keyword(s):  
Trivial Extension

scholarly journals Forecasting intermittent and sparse time series: A unified probabilistic framework via deep renewal processes

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259764
Author(s):  
Ali Caner Türkmen ◽  
Tim Januschowski ◽  
Yuyang Wang ◽  
Ali Taylan Cemgil
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Discrete Time ◽  
Predictive Accuracy ◽  
Demand Forecasting ◽  
Trivial Extension ◽  
Renewal Processes ◽  
Probabilistic Forecasting ◽  
Unified Framework ◽  
Intermittent Demand

Intermittency are a common and challenging problem in demand forecasting. We introduce a new, unified framework for building probabilistic forecasting models for intermittent demand time series, which incorporates and allows to generalize existing methods in several directions. Our framework is based on extensions of well-established model-based methods to discrete-time renewal processes, which can parsimoniously account for patterns such as aging, clustering and quasi-periodicity in demand arrivals. The connection to discrete-time renewal processes allows not only for a principled extension of Croston-type models, but additionally for a natural inclusion of neural network based models—by replacing exponential smoothing with a recurrent neural network. We also demonstrate that modeling continuous-time demand arrivals, i.e., with a temporal point process, is possible via a trivial extension of our framework. This leads to more flexible modeling in scenarios where data of individual purchase orders are directly available with granular timestamps. Complementing this theoretical advancement, we demonstrate the efficacy of our framework for forecasting practice via an extensive empirical study on standard intermittent demand data sets, in which we report predictive accuracy in a variety of scenarios.

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