The functional equationf(xy)=ff(x) xy ff(y) in a partially ordered monoid

1976 ◽  
Vol 14 (1-2) ◽  
pp. 33-35
Author(s):  
F. J. Papp
Keyword(s):  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid

The partially ordered monoid generated by the operators H, S, P u , P f on classes of algebras

2009 ◽  
Vol 62 (4) ◽  
pp. 351-365
Author(s):  
Boža Tasić
Keyword(s):  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid

scholarly journals On the Partially Ordered Monoid Generated by the Operators H, S, P, Ps on Classes of Algebras

2001 ◽  
Vol 245 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Boža Tasić
Keyword(s):  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid

Monoid based semantics for linear formulas

2001 ◽  
Vol 66 (4) ◽  
pp. 1597-1619 ◽  
Author(s):  
W. P. R. Mitchell ◽  
H. Simmons
Keyword(s):  
Ordered Group ◽  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Group ◽  
Girard Quantale ◽  
Partially Ordered Monoid

Abstract.Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.

Monoid based semantics for linear formulas (corrected republication)

2002 ◽  
Vol 67 (2) ◽  
pp. 505-527
Author(s):  
W. P. R. Mitchell ◽  
H. Simmons
Keyword(s):  
Ordered Group ◽  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Group ◽  
Girard Quantale ◽  
Partially Ordered Monoid

AbstractEach Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.

scholarly journals Guaranteed Scoring Games

10.37236/5417 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Urban Larsson ◽  
Richard J. Nowakowski ◽  
João P. Neto ◽  
Carlos P. Santos
Keyword(s):  
Congruence Class ◽  
Order Relation ◽  
Combinatorial Games ◽  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid ◽  
Congruence Classes

The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor (1953), Ettinger (1996) and Johnson (2014). We present the structure of GS and the techniques needed to analyze a sum of guaranteed games. Firstly, GS form a partially ordered monoid, via defined Right- and Left-stops over the reals, and with disjunctive sum as the operation. In fact, the structure is a quotient monoid with partially ordered congruence classes. We show that there are four reductions that when applied, in any order, give a unique representative for each congruence class. The monoid is not a group, but in this paper we prove that if a game has an inverse it is obtained by 'switching the players'. The order relation between two games is defined by comparing their stops in any disjunctive sum. Here, we demonstrate how to compare the games via a finite algorithm instead, extending ideas of Ettinger, and also Siegel (2013).

scholarly journals Examples of Pomonoids of Full Transformations of a Poset

2022 ◽  
pp. 1-4
Author(s):  
Bana Al Subaiei
Keyword(s):  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid

In this research, the partially ordered monoid (simple pomonoid) full transformations of a poset O(X) is studied, and some related properties are examined. We show that when the poset X_ is not totally ordered, the pomonoid of all decreasing singular self-maps of a poset X_ (denoted by S^-) and the pomonoid of all increasing singular self-maps of a poset X_ (denoted by S^+) may not be generally isomorphic. Some specific partial ordered relations are considered, and the cardinalities of S^- and S^+ under these relations are found. The set of fixed, decreasing, and increasing points of mapping α in O(X) are also investigated. KEYWORDS Posets, pomonoids, full transformations

The functional equationf(xy)=ff(x) xyff(y) in a partially ordered monoid

1975 ◽  
Vol 12 (1) ◽  
pp. 116-116
Author(s):  
F. J. Papp
Keyword(s):  
Partially Ordered ◽  
Ordered Monoid ◽  
Partially Ordered Monoid

Quasi-injectivity of partially ordered acts

2020 ◽  
pp. 2250047
Author(s):  
Mahdieh Yavari ◽  
M. Mehdi Ebrahimi
Keyword(s):  
Ordered Sets ◽  
Partially Ordered ◽  
Ordered Monoid ◽  
Injective Modules

It is well known that injective objects play a fundamental role in many branches of mathematics. The question whether a given category has enough injective objects has been investigated for many categories. Also, quasi-injective modules and acts have been studied by many categorists. In this paper, we study quasi-injectivity in the category of actions of an ordered monoid on ordered sets ([Formula: see text]) with respect to embeddings. Also, we give the relation between injectivity, quasi-injectivity (with respect to embeddings), and poset completeness in the category [Formula: see text] and some of its important subcategories.

Abian's poset and the ordered monoid of annihilator classes in a reduced commutative ring

2014 ◽  
Vol 13 (08) ◽  
pp. 1450070 ◽  
Author(s):  
David F. Anderson ◽  
John D. LaGrange
Keyword(s):  
Commutative Ring ◽  
Equivalence Relation ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Equivalence Classes ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Ordered Monoid

Let R be a reduced commutative ring with 1 ≠ 0. Then R is a partially ordered set under the Abian order defined by x ≤ y if and only if xy = x2. Let RE be the set of equivalence classes for the equivalence relation on R given by x ~ y if and only if ann R(x) = ann R(y). Then RE is a commutative Boolean monoid with multiplication [x][y] = [xy] and is thus partially ordered by [x] ≤ [y] if and only if [xy] = [x]. In this paper, we study R and RE as both monoids and partially ordered sets. We are particularly interested in when RE can be embedded in R as either a monoid or a partially ordered set.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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