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On the Topological Structure of the (Non-) Finitely-generated Locus of Frobenius Algebras emerging from Stanley-Reisner Rings
Edisson Gallego, Juan D. Vélez, Sergio D. Molina-Aristizabal +2
In this paper we study initial topological properties of the (non-)finitely-generated locus of Frobenius Algebra coming from Stanley-Reisner rings defined through face ideals. More…
On Preservation Properties and a Special Algebraic Characterization of Some Stronger Forms of the Noetherian Condition
Danny A. J. Gomez-Ramirez, Juan D. Velez, Edisson Gallego
We give an elementary proof prove of the preservation of the Noetherian condition for commutative rings with unity having at least one finitely generated ideal such that th…
Generalizations of the Direct Summand Theorem over UFD-s for some Bigenerated Extensions and an Asymptotic Version of Koh's Conjecture
Danny A. J. Gomez-Ramirez, Edisson Gallego, Juan D. Velez
This article deals with two different problems in commutative algebra. In the first part, we give a proof of generalized forms of the Direct Summand Theorem (DST (or DCS)) for modu…
Containment-Division Rings and New Characterizations of Dedekind Domains
Danny A. J. Gomez-Ramirez, Juan D. Velez, Edisson Gallego
We introduce a new class of commutative rings with unity, namely, the Containment-Division Rings (CDR-s). We show that this notion has a very exceptional origin since it was essent…
Towards an Homological Generalization of the Direct Summand Theorem
Juan D. Velez, Danny A. J. Gomez-Ramirez
We present a more general (parametric-) homological characterization of the Direct Summand Theorem. Specifically, we state two new conjectures: the Socle-Parameter conjecture (SPC)…
Normality and Related Properties of Forcing Algebras
Danny A. J. Gomez-Ramirez, Holger Brenner
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing alg…