scholarly journals Coefficient rings of numerical semigroup algebras

2021 ◽  
Author(s):  
I-Chiau Huang ◽  
Raheleh Jafari
Keyword(s):  
Numerical Semigroup ◽  
Semigroup Algebras

Numerical semigroup algebras

2019 ◽  
Vol 48 (3) ◽  
pp. 1079-1088
Author(s):  
I-Chiau Huang ◽  
Mee-Kyoung Kim
Keyword(s):  
Numerical Semigroup ◽  
Semigroup Algebras

scholarly journals Factorizations in numerical semigroup algebras

2019 ◽  
Vol 223 (5) ◽  
pp. 2258-2272
Author(s):  
I-Chiau Huang ◽  
Raheleh Jafari
Keyword(s):  
Numerical Semigroup ◽  
Semigroup 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 Canonical trace ideal and residue for numerical semigroup rings

2021 ◽  
Author(s):  
Jürgen Herzog ◽  
Takayuki Hibi ◽  
Dumitru I. Stamate
Keyword(s):  
Numerical Semigroup ◽  
Semigroup Rings ◽  
Trace Ideal ◽  
Numerical Semigroup Rings

On the numerical semigroup generated by {bn+1+i+bn+i−1b−1∣i∈N}$\begin{array}{} \{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\} \end{array}$

2020 ◽  
Vol 30 (4) ◽  
pp. 257-264
Author(s):  
Ze Gu
Keyword(s):  
Numerical Semigroup ◽  
Frobenius Number ◽  
Embedding Dimension ◽  
Order Relations ◽  
Positive Integers

AbstractLet b, n be two positive integers such that b ≥ 2, and S(b, n) be the numerical semigroup generated by $\begin{array}{} \{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\} \end{array}$. Applying two order relations, we give formulas for computing the embedding dimension, the Frobenius number, the type and the genus of S(b, n).

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
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