Certain partitions on a set and their applications to different classes of graded algebras

Martín, Antonio J. Calderón, and Dieme, Boubacar. "Certain partitions on a set and their applications to different classes of graded algebras." Communications in Mathematics 29.2 (2021): 243-254. <http://eudml.org/doc/298074>.

@article{Martín2021,
abstract = {Let $(\{\mathfrak \{A\}\} , \{\epsilon \}_\{u\})$ and $(\{\mathfrak \{B\}\} , \{\epsilon \}_\{b\})$ be two pointed sets. Given a family of three maps $\{\mathcal \{F\}\}=\lbrace f_1\colon \{\{\mathfrak \{A\}\} \} \rightarrow \{\mathfrak \{A\}\} ; f_2\colon \{\{\mathfrak \{A\}\} \} \times \{\mathfrak \{A\}\} \rightarrow \{\mathfrak \{A\}\} ; f_3\colon \{\{\mathfrak \{A\}\} \} \times \{\mathfrak \{A\}\} \rightarrow \{\mathfrak \{B\}\} \rbrace $, this family provides an adequate decomposition of $\{\mathfrak \{A\}\} \setminus \lbrace \epsilon _u \rbrace $ as the orthogonal disjoint union of well-described $\{\mathcal \{F\}\}$-invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak $H^*$-algebras.},
author = {Martín, Antonio J. Calderón, Dieme, Boubacar},
journal = {Communications in Mathematics},
keywords = {Set; application; graded algebra; involutive algebra; quadratic algebra; weak $H^*$-algebra; structure theory},
language = {eng},
number = {2},
pages = {243-254},
publisher = {University of Ostrava},
title = {Certain partitions on a set and their applications to different classes of graded algebras},
url = {http://eudml.org/doc/298074},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Martín, Antonio J. Calderón
AU - Dieme, Boubacar
TI - Certain partitions on a set and their applications to different classes of graded algebras
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 243
EP - 254
AB - Let $({\mathfrak {A}} , {\epsilon }_{u})$ and $({\mathfrak {B}} , {\epsilon }_{b})$ be two pointed sets. Given a family of three maps ${\mathcal {F}}=\lbrace f_1\colon {{\mathfrak {A}} } \rightarrow {\mathfrak {A}} ; f_2\colon {{\mathfrak {A}} } \times {\mathfrak {A}} \rightarrow {\mathfrak {A}} ; f_3\colon {{\mathfrak {A}} } \times {\mathfrak {A}} \rightarrow {\mathfrak {B}} \rbrace $, this family provides an adequate decomposition of ${\mathfrak {A}} \setminus \lbrace \epsilon _u \rbrace $ as the orthogonal disjoint union of well-described ${\mathcal {F}}$-invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak $H^*$-algebras.
LA - eng
KW - Set; application; graded algebra; involutive algebra; quadratic algebra; weak $H^*$-algebra; structure theory
UR - http://eudml.org/doc/298074
ER -