The incidence algebra of a group reduced partially ordered set

1980 ◽  
pp. 148-156
Author(s):  
Phil Hanlon
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Incidence Algebra

scholarly journals Some chain conditions on weak incidence algebras

2005 ◽  
Vol 2005 (15) ◽  
pp. 2389-2397
Author(s):  
Surjeet Singh ◽  
Fawzi Al-Thukair
Keyword(s):  
Commutative Ring ◽  
Partially Ordered Set ◽  
Nonempty Subset ◽  
Ordered Set ◽  
Partially Ordered ◽  
Incidence Algebra ◽  
Chain Conditions ◽  
Incidence Algebras

LetXbe any partially ordered set,Rany commutative ring, andT=I∗(X,R)the weak incidence algebra ofXoverR. LetZbe a finite nonempty subset ofX,L(Z)={x∈X:x≤z   for some   z∈Z}, andM=Tez. Various chain conditions onMare investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.

scholarly journals Kongruensi Unsur Idempoten Ortogonal dalam Aljabar Insidensi Finitary

2012 ◽  
Vol 13 (2) ◽  
pp. 89
Author(s):  
Ema Carnia ◽  
Sri Wahyuni ◽  
Irawati Irawati ◽  
Setiadji Setiadji
Keyword(s):  
Commutative Ring ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Incidence Algebra

Let X be a partially ordered set, R is a commutative ring with identity and FININC (X, R) denote finitary incidencealgebra of poset X over R. In this paper it will be seen congruence of two elements that are idempotent orthogonalin FININC (X, R) relative to the modulo Radical Jacobson of algebra. Review of this topic would be useful to examineisomorphism problems of the finitary incidence Algebra.

scholarly journals Essential ideals of incidence algebras

2000 ◽  
Vol 68 (2) ◽  
pp. 252-260 ◽  
Author(s):  
Eugene Spiegel
Keyword(s):  
Commutative Ring ◽  
Left Ideal ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Locally Finite ◽  
Partially Ordered ◽  
Incidence Algebra ◽  
Incidence Algebras ◽  
Essential Ideal ◽  
Finite Partially Ordered Set

AbstractIt is determined when there exists a minimal essential ideal, or minimal essential left ideal, in the incidence algebra of a locally finite partially ordered set defined over a commutative ring. When such an ideal exists, it is described.

scholarly journals A remark on the extension of the concept of incidence algebras to nonlocally finite partially ordered sets

2004 ◽  
Vol 2004 (40) ◽  
pp. 2145-2147
Author(s):  
Boniface I. Eke
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Incidence Algebra ◽  
Incidence Algebras ◽  
Finite Partially Ordered Set

An incidence algebra of a nonlocally finite partially ordered setQis a very rare concept, perhaps nonexistent. In this note, we will attempt to construct such an algebra.

Information Retrieval Systems, an Algebraic Approach I1

1981 ◽  
Vol 4 (3) ◽  
pp. 551-603
Author(s):  
Zbigniew Raś
Keyword(s):  
Information Retrieval ◽  
Boolean Algebra ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Algebraic Approach ◽  
Partially Ordered ◽  
Retrieval Systems ◽  
Information Retrieval Systems ◽  
Present Part ◽  
L Systems

This paper is the first of the three parts of work on the information retrieval systems proposed by Salton (see [24]). The system is defined by the notions of a partially ordered set of requests (A, ⩽), the set of objects X and a monotonic retrieval function U : A → 2X. Different conditions imposed on the set A and a function U make it possible to obtain various classes of information retrieval systems. We will investigate systems in which (A, ⩽) is a partially ordered set, a lattice, a pseudo-Boolean algebra and Boolean algebra. In my paper these systems are called partially ordered information retrieval systems (po-systems) lattice information retrieval systems (l-systems); pseudo-Boolean information retrieval systems (pB-systems) and Boolean information retrieval systems (B-systems). The first part concerns po-systems and 1-systems. The second part deals with pB-systems and B-systems. In the third part, systems with a partial access are investigated. The present part discusses the method for construction of a set of attributes. Problems connected with the selectivity and minimalization of a set of attributes are investigated. The characterization and the properties of a set of attributes are given.

scholarly journals Each join-completion of a partially ordered set in the solution of a universal problem

1974 ◽  
Vol 17 (4) ◽  
pp. 406-413 ◽  
Author(s):  
Jürgen Schmidt
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Unique Extension ◽  
Partially Ordered ◽  
Special Cases

The main result of this paper is the theorem in the title. Only special cases of it seem to be known so far. As an application, we obtain a result on the unique extension of Galois connexions. As a matter of fact, it is only by the use of Galois connexions that we obtain the main result, in its present generality.

scholarly journals Primitive idempotent measures on compact semitopological semigroups

1972 ◽  
Vol 13 (4) ◽  
pp. 451-455 ◽  
Author(s):  
Stephen T. L. Choy
Keyword(s):  
Partial Order ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Zero Element ◽  
Primitive Idempotent ◽  
Natural Partial Order ◽  
Partially Ordered

For a semigroup S let I(S) be the set of idempotents in S. A natural partial order of I(S) is defined by e ≦ f if ef = fe = e. An element e in I(S) is called a primitive idempotent if e is a minimal non-zero element of the partially ordered set (I(S), ≦). It is easy to see that an idempotent e in S is primitive if and only if, for any idempotent f in S, f = ef = fe implies f = e or f is the zero element of S. One may also easily verify that an idempotent e is primitive if and only if the only idempotents in eSe are e and the zero element. We let П(S) denote the set of primitive idempotent in S.

ON RIBBON PRESENTATIONS OF RIBBON KNOTS

1994 ◽  
Vol 03 (02) ◽  
pp. 223-231
Author(s):  
TOMOYUKI YASUDA
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Totally Ordered Set

A ribbon n-knot Kn is constructed by attaching m bands to m + 1n-spheres in the Euclidean (n + 2)-space. There are many way of attaching them; as a result, Kn has many presentations which are called ribbon presentations. In this note, we will induce a notion to classify ribbon presentations for ribbon n-knots of m-fusions (m ≥ 1, n ≥ 2), and show that such classes form a totally ordered set in the case of m = 2 and a partially ordered set in the case of m ≥ 1.

scholarly journals Spherical posets from commuting elements

2018 ◽  
Vol 21 (4) ◽  
pp. 593-628 ◽  
Author(s):  
Cihan Okay
Keyword(s):  
Homotopy Type ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Classifying Space ◽  
Partially Ordered ◽  
Abelian Subgroups

AbstractIn this paper, we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial p-group. We prove that the universal cover of its nerve is homotopy equivalent to a wedge of r-spheres where {2r\geq 4} is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles as introduced in [2].

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