The Hochschild cohomology rings of the numerical semigroup algebras of embedding dimension two

2020 ◽  
Vol 224 (3) ◽  
pp. 1320-1339
Author(s):  
Emil Sköldberg ◽  
Nghia T.H. Tran
Keyword(s):  
Hochschild Cohomology ◽  
Numerical Semigroup ◽  
Embedding Dimension ◽  
Semigroup Algebras ◽  
Cohomology 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).

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 Measuring primality in numerical semigroups with embedding dimension three

2015 ◽  
Vol 15 (01) ◽  
pp. 1650007 ◽  
Author(s):  
S. T. Chapman ◽  
P. A. García-Sánchez ◽  
Z. Tripp ◽  
C. Viola
Keyword(s):  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Catenary Degree

In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree.

scholarly journals THE HOCHSCHILD COHOMOLOGY RING OF A CLASS OF SPECIAL BISERIAL ALGEBRAS

2010 ◽  
Vol 09 (01) ◽  
pp. 73-122 ◽  
Author(s):  
NICOLE SNASHALL ◽  
RACHEL TAILLEFER
Keyword(s):  
London Math ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Krull Dimension ◽  
Finitely Generated ◽  
Cohomology Rings ◽  
Hochschild Cohomology Ring ◽  
Special Biserial Algebras ◽  
Support Varieties

We consider a class of self-injective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of dΛN is a finitely generated K-algebra. Moreover, the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative K-algebra of Krull dimension two. As a consequence the conjecture of [N. Snashall and Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc.88 (2004) 705–732], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.

Delta sets for nonsymmetric numerical semigroups with embedding dimension three

2018 ◽  
Vol 30 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
David Llena ◽  
Alessio Moscariello
Keyword(s):  
Fast Algorithm ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Delta Set

Abstract We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroup with embedding dimension three. We also characterize the sets of integers that are the Delta set of a numerical semigroup of this kind.

scholarly journals Module and Hochschild cohomology of certain semigroup algebras

2015 ◽  
Vol 49 (4) ◽  
pp. 315-318
Author(s):  
A. Shirinkalam ◽  
A. Pourabbas ◽  
M. Amini
Keyword(s):  
Hochschild Cohomology ◽  
Semigroup Algebras
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