Frobenius and Cartier Algebras of Stanley–Reisner Rings (II)

Autor:	Santiago Zarzuela, Alberto F. Boix
Rok vydání:	2019
Předmět:	Ring (mathematics) Pure mathematics Mathematics::Commutative Algebra Formal power series General Mathematics Zero (complex analysis) Monomial ideal Simplicial complex symbols.namesake Residue field Frobenius algebra symbols Injective hull Mathematics
Zdroj:	Acta Mathematica Vietnamica. 44:571-586
ISSN:	2315-4144 0251-4184
DOI:	10.1007/s40306-018-00314-1
Popis:	It is known that the Frobenius algebra of the injective hull of the residue field of a complete Stanley–Reisner ring (i.e., a formal power series ring modulo a squarefree monomial ideal) can be only principally generated or infinitely generated as algebra over its degree zero piece, and that this fact can be read off in the corresponding simplicial complex; in the infinite case, we exhibit a 1–1 correspondence between potential new generators appearing on each graded piece and certain pairs of faces of such a simplicial complex, and we use it to provide an alternative proof of the fact that these Frobenius algebras can only be either principally generated or infinitely generated.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::66dff3758a8dfd8f132b1c0230f8c970 https://doi.org/10.1007/s40306-018-00314-1 Zobrazit plný text záznamu Full text from SpringerLink