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 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 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 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.

scholarly journals Posets and differential graded algebras

1998 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Jacqui Ramagge ◽  
Wayne W. Wheeler
Keyword(s):  
Commutative Ring ◽  
Partially Ordered Set ◽  
Integral Domain ◽  
Ordered Set ◽  
Order Relation ◽  
Graded Algebras ◽  
Partially Ordered ◽  
Differential Graded Algebras ◽  
Finite Posets

AbstractIf P is a partially ordered set and R is a commutative ring, then a certain differential graded R-algebra A•(P) is defined from the order relation on P. The algebra A•() corresponding to the empty poset is always contained in A•(P) so that A•(P) can be regarded as an A•()-algebra. The main result of this paper shows that if R is an integral domain and P and P′ are finite posets such that A•(P)≅A•(P′) as differential graded A•()-algebras, then P and P′ are isomorphic.

The Ordering of Spec R

1976 ◽  
Vol 28 (4) ◽  
pp. 820-835 ◽  
Author(s):  
William J. Lewis ◽  
Jack Ohm
Keyword(s):  
Commutative Ring ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Prime Ideals ◽  
Ordered Sets ◽  
Partially Ordered

Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]).

Classification of involutions on finitary incidence algebras

2014 ◽  
Vol 24 (08) ◽  
pp. 1085-1098 ◽  
Author(s):  
Rosali Brusamarello ◽  
Érica Zancanella Fornaroli ◽  
Ednei Aparecido Santulo
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Multilinear Algebra ◽  
Partially Ordered ◽  
Incidence Algebras ◽  
Linear Multilinear Algebra ◽  
Necessary And Sufficient

Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI (X), to be equivalent in the case when every multiplicative automorphism of FI (X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181–188] for finitary incidence algebras.

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.

The Periodic Radical of Group Rings and Incidence Algebras

1998 ◽  
Vol 41 (4) ◽  
pp. 481-487 ◽  
Author(s):  
M. M. Parmenter ◽  
E. Spiegel ◽  
P. N. Stewart
Keyword(s):  
Group Ring ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Group Rings ◽  
Locally Finite ◽  
Partially Ordered ◽  
Incidence Algebras ◽  
Finite Partially Ordered Set ◽  
Necessary And Sufficient

AbstractLet R be a ring with 1 and P(R) the periodic radical of R. We obtain necessary and sufficient conditions for P(RG) = 0 when RG is the group ring of an FC group G and R is commutative. We also obtain a complete description of when I(X, R) is the incidence algebra of a locally finite partially ordered set X and R is commutative.

scholarly journals Chain conditions on posets

1974 ◽  
Vol 15 (1) ◽  
pp. 79-81
Author(s):  
Cynthia D. Geoffroy ◽  
H. E. Scheiblich
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Chain Condition ◽  
Partially Ordered ◽  
Chain Conditions ◽  
Standard Lattice

The aim of this note is to generalize to an arbitrary partially ordered set (poset) (P, ≦) the standard lattice results on the Jordan–Dedekind Chain Condition (abbreviated hereafter to J.D.C.C.). Birkhoff [1] defines semimodularity for a lattice L by(ξ) if x, y cover a and x # y, then x ∨ y covers x and y.

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