1 citations · 2 across the 9 of their papers we have counts for
9 papers
Functional Conceptual Substratum as a New Cognitive Mechanism for Mathematical Creation
Danny A. J. Gomez-Ramirez, Stefan Hetzl
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we prese…
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…
A General Version of the Nullstellensatz for Arbitrary Fields
Juan D. Velez, Danny A. J. Gomez-Ramirez, Edisson Gallego
We prove a general version of Bezout's form of the Nullstellensatz for arbitrary fields. The corresponding sufficient and necessary condition only involves the local existence of m…
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)…