No Fixed Ideal of Society

2017 ◽  
pp. 362-364
Author(s):  
George Santayana ◽  
John McCormick
Keyword(s):  
Fixed Ideal

MODEL OF SOCIAL POTENTIAL OF CHILDHOOD IN THE RUSSIAN REGIONS: THE RESULTS OF EXPERIMENTS

2019 ◽  
pp. 152-162
Author(s):  
A.G. Filipova ◽  
A.V. Vysotskaya
Keyword(s):  
Third Wave ◽  
Russian Regions ◽  
The Third ◽  
Control Factors ◽  
Social Potential ◽  
System Input ◽  
Optimal Values ◽  
Fixed Ideal ◽  
And Control ◽  
Selection Of

The article presents the results of mathematical experiments with the system «Social potential of childhood in the Russian regions». In the structure of system divided into three subsystems – the «Reproduction of children in the region», «Children’s health» and «Education of children», for each defined its target factor (output parameter). The groups of infrastructure factors (education, health, culture and sport, transport), socio-economic, territorial-settlement, demographic and en-vironmental factors are designated as the factors that control the system (input parameters). The aim of the study is to build a model îf «Social potential of childhood in the Russian regions», as well as to conduct experiments to find the optimal ratio of the values of target and control factors. Three waves of experiments were conducted. The first wave is related to the analysis of the dynam-ics of indicators for 6 years. The second – with the selection of optimal values of control factors at fixed ideal values of target factors. The third wave allowed us to calculate the values of the target factors based on the selected optimal values of the control factors of the previous wave.

On Rings of Fractions

1970 ◽  
Vol 13 (4) ◽  
pp. 425-430 ◽  
Author(s):  
T. M. K. Davison
Keyword(s):  
Noetherian Ring ◽  
Multiplicative System ◽  
Topological Ring ◽  
Commutative Noetherian Ring ◽  
Image Position ◽  
Fixed Ideal

Let R be a commutative Noetherian ring with identity, and let M be a fixed ideal of R. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in R, and let j = js: R → S-1R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S-1R is a topological ring in ihe j(M)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂ p(S), whereHence S-1R is a topological ring for all S if and only if M ⊂ p*(R), where

scholarly journals Alternative polarizations of Borel fixed ideals

2012 ◽  
Vol 207 ◽  
pp. 79-93 ◽  
Author(s):  
Kohji Yanagawa
Keyword(s):  
Polynomial Ring ◽  
Monomial Ideal ◽  
Simplicial Complexes ◽  
Regular Sequence ◽  
Fixed Ideal

AbstractFor a monomial idealIof a polynomial ringS, apolarizationofIis a square-free monomial idealJof a larger polynomial ringsuch thatS/Iis a quotient of/Jby a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sendsours sends it tox1y2y3Using this idea, we recover/refine the results onsquare-free operationin the shifting theory of simplicial complexes. The present paper generalizes a result of Nagel and Reiner, although our approach is very different.

Elimination from Homogeneous Polynomials Over a Polynomial Ring

1976 ◽  
Vol 28 (6) ◽  
pp. 1269-1276
Author(s):  
John G. Stevens
Keyword(s):  
Polynomial Ring ◽  
Homogeneous Polynomials ◽  
Fixed Ideal

Let Ω be a field and Γ a parameter. We designate the set of all polynomials homogeneous in (X) = (X1, … , Xn) with coefficients in Ω [Γ] by H Ω Γ[X] and write such polynomials as F, F(X), or F(X, Γ). The degree of a polynomial in H Ω Γ [X] shall mean the degree in (X). Let I = (F1 … , Fr) be a fixed ideal in H Ω Γ [X] generated by F1 … , Fr.

scholarly journals I-Semiprime Submodules

2019 ◽  
pp. 2030-2035
Author(s):  
Adwia J. Abdul-AlKhalik
Keyword(s):  
Commutative Ring ◽  
Prime Submodule ◽  
Fixed Ideal

 Let  be a commutative ring with identity and a fixed ideal of  and  be an unitary -module.We say that a proper submodule  of  is -semi prime submodule if with . In this paper, we investigate some properties of this class of submodules. Also, some characterizations of -semiprime submodules will be given, and we show that under some assumptions -semiprime submodules and semiprime submodules are coincided.

scholarly journals A remark on the distributive law for an ideal in a commutative ring

1966 ◽  
Vol 7 (4) ◽  
pp. 193-198 ◽  
Author(s):  
C. U. Jensen
Keyword(s):  
Commutative Ring ◽  
Identity Element ◽  
Prime Ideals ◽  
Distributive Law ◽  
Image Position ◽  
Fixed Ideal

Let R be a commutative ring, with an identity element. It is the purpose of this note to establish conditions for an arbitrary but fixed ideal a of R to satisfy the distributive lawfor all ideals b and c of R. In particular, in the Noetherian case, this will be related to the decomposition of a into prime ideals. We start withProposition 1. For a fixed ideal a in a commutative ring R with an identity element, the following conditions are equivalent.

A construction of Prüfer rings involving quotients of Rees algebras

2018 ◽  
Vol 17 (06) ◽  
pp. 1850098
Author(s):  
Carmelo Antonio Finocchiaro
Keyword(s):  
Rees Algebra ◽  
Rees Algebras ◽  
Fixed Ideal ◽  
Prüfer Rings

A family of quotients of a Rees algebra associated to a ring with respect to a fixed ideal was recently introduced by Barucci, D’Anna and Strazzanti. In this paper, we will classify rings of this family that satisfy certain Prüfer-like properties and, as a particular case, we will extend results obtained for amalgamated duplications and Nagata idealizations.

Making and Breaking Mathematical Sense

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Social Constraints ◽  
Cognitive Studies ◽  
Human Endeavor ◽  
Institutional Contexts ◽  
Underlying Reality ◽  
Fixed Ideal ◽  
Changes Over Time ◽  
Mathematical Signs

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? This book combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, the book challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics' exceptional consensus is due to the subject's underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

scholarly journals I-Nearly Prime Submodules

2019 ◽  
pp. 2468-2472
Author(s):  
Adwia J. Abdul-AlKalik ◽  
Nuhad S. Al-Mothafar
Keyword(s):  
Commutative Ring ◽  
Prime Submodules ◽  
Unitary Module ◽  
Fixed Ideal

     Let  be a commutative ring with identity, and a fixed ideal of  and  be an unitary -module. In this paper we  introduce and study the concept of -nearly prime submodules as genrealizations of nearly prime and we investigate some properties of this class of submodules. Also, some characterizations of -nearly prime submodules will be given.

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