scholarly journals Regular algebras of dimension 4 with 3 generators

2012 ◽  
pp. 221-241 ◽  
Author(s):  
D. Rogalski ◽  
J. Zhang
Keyword(s):  
Regular Algebras

scholarly journals Dynamic Łukasiewicz logic and its application to immune system

2021 ◽  
Author(s):  
Antonio Di Nola ◽  
Revaz Grigolia ◽  
Nunu Mitskevich ◽  
Gaetano Vitale
Keyword(s):  
Immune System ◽  
Scalar Multiplication ◽  
Kripke Semantics ◽  
Łukasiewicz Logic ◽  
Lukasiewicz Logic ◽  
Regular Algebras

AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ I D Ł n on the base of n-valued Łukasiewicz logic $${\L }_n$$ Ł n and corresponding to it immune dynamic $$MV_n$$ M V n -algebra ($$IDL_n$$ I D L n -algebra), $$1< n < \omega $$ 1 < n < ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ ( M , R , ◊ ) that combine the varieties of $$MV_n$$ M V n -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ M = ( M , ⊕ , ⊙ , ∼ , 0 , 1 ) and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ R = ( R , ∪ , ; , ∗ ) into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$ ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ I D Ł n with application in immune system.

Artin–Schelter regular algebras of dimension five with three generators

2021 ◽  
pp. 2250235
Author(s):  
Jun Li
Keyword(s):  
Dimension Formula ◽  
Regular Algebras ◽  
Generating Relations ◽  
Degree Type

In this paper, we investigate Artin–Schelter regular algebras of dimension [Formula: see text] with three generators in degree [Formula: see text] under the hypothesis that [Formula: see text], in which the degree types of the relations for the number of the generating relations less than five can be determined. We prove that the only possible degree type of three generating relations is [Formula: see text] and the only possible degree type of four generating relations is [Formula: see text].

scholarly journals Regular algebras of dimension 4 and their $A_\infty$ -Ext-algebras

2007 ◽  
Vol 137 (3) ◽  
pp. 537-584 ◽  
Author(s):  
D.-M. Lu ◽  
J. H. Palmieri ◽  
Q.-S. Wu ◽  
J. J. Zhang
Keyword(s):  
Regular Algebras

HOMOGENEOUS PBW DEFORMATION FOR ARTIN–SCHELTER REGULAR ALGEBRAS

2014 ◽  
Vol 91 (1) ◽  
pp. 53-68 ◽  
Author(s):  
Y. SHEN ◽  
G.-S. ZHOU ◽  
D.-M. LU
Keyword(s):  
Regular Algebras

AbstractWe introduce a method named homogeneous PBW deformation that preserves the regularity and some other homological properties for multigraded algebras. The method is used to produce Artin–Schelter regular algebras without the hypothesis on grading.

Derivations in Commutative Regular Algebras

2004 ◽  
Vol 75 (3/4) ◽  
pp. 418-419 ◽  
Author(s):  
A. F. Ber ◽  
F. A. Sukochev ◽  
V. I. Chilin
Keyword(s):  
Regular Algebras

scholarly journals Double extension regular algebras of type (14641)

2009 ◽  
Vol 322 (2) ◽  
pp. 373-409 ◽  
Author(s):  
James J. Zhang ◽  
Jun Zhang
Keyword(s):  
Regular Algebras ◽  
Double Extension
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