ON SOME DECOMPOSITION OF THE SUM OF A DIRECT SYSTEM OF ALGEBRAS INTO A SUBDIRECT PRODUCT

1989 ◽  
Vol 22 (1) ◽  
pp. 235-240
Author(s):  
Jerzy Plonka
2001 ◽  
Vol 26 (9) ◽  
pp. 539-545
Author(s):  
P. Mukhopadhyay

Bandelt and Petrich (1982) proved that an inversive semiringSis a subdirect product of a distributive lattice and a ring if and only ifSsatisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the “ring” involved can be gradually enriched to a “field.” Finally, we provide a construction of fullE-inversive semirings, which are subdirect products of a semilattice and a ring.


1987 ◽  
Vol 35 (1) ◽  
pp. 111-123 ◽  
Author(s):  
Henry Heatherly ◽  
Altha Blanchet

A ring for which there is a fixed integer n ≥ 2 such that every element in the ring has an n-th in the ring is called an n-th root ring. This paper gives numerous examples of diverse types of n-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutative n-th root ring with unity. The structure of n-th root rings with chain conditions is developed and finite n-th root rings are completely classified. Subdirect product representations are given for several classes of n-th root rings.


2007 ◽  
Vol E90-B (2) ◽  
pp. 334-337
Author(s):  
L. DING ◽  
Q. YIN ◽  
Y. ZHANG ◽  
Y. MENG

2019 ◽  
Vol 62 (3) ◽  
pp. 799-815 ◽  
Author(s):  
Giulio Codogni

AbstractA polarized variety is K-stable if, for any test configuration, the Donaldson–Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits buildings. We show that the Donaldson–Futaki invariant, conveniently normalized, is a continuous function on this space. We also introduce a pseudo-metric on the space of test configurations. Recall that K-stability can be enhanced by requiring that the Donaldson–Futaki invariant is positive on any admissible filtration of the co-ordinate ring. We show that admissible filtrations give rise to Cauchy sequences of test configurations with respect to the above mentioned pseudo-metric.


Author(s):  
P. R. Jones

AbstractThe main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.


Author(s):  
Brian Janke ◽  
Thomas Kuehn

Thermodynamic analysis has been conducted for geothermal power cycles using a portion of deep ground sequestered CO2 as the working fluid. This allows energy production from much shallower depths and in geologic areas with much lower temperature gradients than those of current geothermal systems. Two different system designs were analyzed for power production with varying reservoir parameters, including reservoir depth, temperature, and CO2 mass flow rate. The first design is a direct single-loop system with the CO2 run directly through the turbine. This system was found to provide higher system efficiency and power production, however design complications such as the need for high pressure turbines, two-phase flow through the turbine and the potential for water-CO2 brine mixtures, could require the use of numerous custom components, driving up the cost. The second design is a binary system using CO2 as the heat transfer fluid to supply thermal energy to an Organic Rankine Cycle (ORC). While this system was found to have slightly less power production and efficiency than the direct system, it significantly reduces the impact of design complications associated with the direct system. This in turn reduces the necessity for certain custom components, thereby reducing system cost. While performance of these two systems is largely dependent on location and operating conditions, the binary system is likely applicable to a larger number of sites and will be more cost effective when used in combination with current off-the-shelf ORC power plants.


2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Štefan Černák ◽  
Judita Lihová

AbstractThe notion of a relatively uniform convergence (ru-convergence) has been used first in vector lattices and then in Archimedean lattice ordered groups.Let G be an Archimedean lattice ordered group. In the present paper, a relative uniform completion (ru-completion) $$ G_{\omega _1 } $$ of G is dealt with. It is known that $$ G_{\omega _1 } $$ exists and it is uniquely determined up to isomorphisms over G. The ru-completion of a finite direct product and of a completely subdirect product are established. We examine also whether certain properties of G remain valid in $$ G_{\omega _1 } $$. Finally, we are interested in the existence of a greatest convex l-subgroup of G, which is complete with respect to ru-convergence.


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