scholarly journals Isomorphisms and derivations of partial flag incidence algebras

2021 ◽  
pp. 1-17
Author(s):  
Mykola Khrypchenko
Keyword(s):  
Unital Ring ◽  
Incidence Algebras ◽  
Finite Posets

Let [Formula: see text] and [Formula: see text] be finite posets and [Formula: see text] a commutative unital ring. In the case where [Formula: see text] is indecomposable, we prove that the [Formula: see text]-linear isomorphisms between partial flag incidence algebras [Formula: see text] and [Formula: see text] are exactly those induced by poset isomorphisms between [Formula: see text] and [Formula: see text]. We also show that the [Formula: see text]-linear derivations of [Formula: see text] are trivial.

scholarly journals Representation-tame incidence algebras of finite posets

2003 ◽  
Vol 96 (2) ◽  
pp. 293-305 ◽  
Author(s):  
Zbigniew Leszczyński
Keyword(s):  
Incidence Algebras ◽  
Finite Posets

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

scholarly journals On the Automorphisms of Incidence Algebras

2001 ◽  
Vol 239 (2) ◽  
pp. 615-623 ◽  
Author(s):  
Eugene Spiegel
Keyword(s):  
Incidence Algebras

Some correlation inequalities in finite posets

Order ◽  
1985 ◽  
Vol 2 (4) ◽  
pp. 387-402 ◽  
Author(s):  
Graham R. Brightwell
Keyword(s):  
Correlation Inequalities ◽  
Finite Posets

Commutative rings and modules that are Nil*-coherent or special Nil*-coherent

2017 ◽  
Vol 16 (10) ◽  
pp. 1750187 ◽  
Author(s):  
Karima Alaoui Ismaili ◽  
David E. Dobbs ◽  
Najib Mahdou
Keyword(s):  
Commutative Rings ◽  
Finitely Generated ◽  
Basic Properties ◽  
Unital Ring ◽  
Reduced Ring ◽  
Coherent Ring ◽  
Ring Extensions ◽  
Coherent Rings ◽  
Finitely Presented

Recently, Xiang and Ouyang defined a (commutative unital) ring [Formula: see text] to be Nil[Formula: see text]-coherent if each finitely generated ideal of [Formula: see text] that is contained in Nil[Formula: see text] is a finitely presented [Formula: see text]-module. We define and study Nil[Formula: see text]-coherent modules and special Nil[Formula: see text]-coherent modules over any ring. These properties are characterized and their basic properties are established. Any coherent ring is a special Nil[Formula: see text]-coherent ring and any special Nil[Formula: see text]-coherent ring is a Nil[Formula: see text]-coherent ring, but neither of these statements has a valid converse. Any reduced ring is a special Nil[Formula: see text]-coherent ring (regardless of whether it is coherent). Several examples of Nil[Formula: see text]-coherent rings that are not special Nil[Formula: see text]-coherent rings are obtained as byproducts of our study of the transfer of the Nil[Formula: see text]-coherent and the special Nil[Formula: see text]-coherent properties to trivial ring extensions and amalgamated algebras.

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