Differential algebras on semigroup algebras

2001 ◽  
pp. 207-226 ◽  
Author(s):  
Mutsumi Saito ◽  
William N. Traves
Keyword(s):  
Semigroup Algebras ◽  
Differential Algebras

Spectra in Some Inverse Semigroup Algebras

2004 ◽  
Vol 104 (2) ◽  
pp. 211-218 ◽  
Author(s):  
M. J. Crabb ◽  
J. Duncan ◽  
C. M. McGregor
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals Homological dimension in semigroup algebras

1971 ◽  
Vol 18 (3) ◽  
pp. 404-413 ◽  
Author(s):  
William R Nico
Keyword(s):  
Homological Dimension ◽  
Semigroup Algebras

On A Multiplicativity up to Homotopy of the Gugenheim Map

2002 ◽  
Vol 9 (3) ◽  
pp. 549-566
Author(s):  
Z. Kharebava
Keyword(s):  
Cochain Complex ◽  
Differential Algebras ◽  
Graded Coalgebra

Abstract In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ 𝑖} : 𝐴* → 𝐶* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐵𝐴*, dBA , Δ,) and (𝐵𝐶*, dBC* , Δ,) carry multiplications. We show that the Gugenheim's map 𝐵{ρ 𝑖} : (𝐵𝐴*, dBA* , Δ,) → (𝐵𝐶*, dBC* , Δ,) is multiplicative up to homotopy with respect to these structures.

scholarly journals On integro-differential algebras

2014 ◽  
Vol 218 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Li Guo ◽  
Georg Regensburger ◽  
Markus Rosenkranz
Keyword(s):  
Differential Algebras

scholarly journals Optimal embeddings of ultradistributions into differential algebras

2017 ◽  
Vol 186 (3) ◽  
pp. 407-438 ◽  
Author(s):  
Andreas Debrouwere ◽  
Hans Vernaeve ◽  
Jasson Vindas
Keyword(s):  
Differential Algebras
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