A Few Remarkable TEM Facts

A few facts on integrality

The purpose of this note is to collect some theorems and proofs related to integrality in commutative algebra. The note is subdivided into three parts. Part 1 (Integrality over rings) consists of known facts (Theorems 1, 4, 5) and a generalized exercise from [1] (Corollary 3) with a few minor variations (Theorem 2 and Corollary 6). Part 2 (Integrality over ideal semifiltrations) merges integral...

A few new (?) facts about infinite elements

We discuss the (conjugated) Bubnov–Galerkin and Petrov–Galerkin infinite element (IE) discretizations to Helmholtz equation including the use of elements of locally variable order, optimal choice of IE shape functions, calculation of Echo Area (EA), and automatic hp-adaptivity. The discussion is illustrated with 2D numerical experiments. 2005 Elsevier B.V. All rights reserved. MSC classificatio...

A few facts on integrality * DETAILED

The purpose of this note is to collect some theorems and proofs related to integrality in commutative algebra. The note is subdivided into four parts. Part 1 (Integrality over rings) consists of known facts (Theorems 1, 4, 5) and a generalized exercise from [1] (Corollary 3) with a few minor variations (Theorem 2 and Corollary 6). Part 2 (Integrality over ideal semifiltrations) merges integrali...

A few facts on integrality * BRIEF

The purpose of this note is to collect some theorems and proofs related to integrality in commutative algebra. The note is subdivided into four parts. Part 1 (Integrality over rings) consists of known facts (Theorems 1, 4, 5) and a generalized exercise from [1] (Corollary 3) with a few minor variations (Theorem 2 and Corollary 6). Part 2 (Integrality over ideal semifiltrations) merges integrali...

Spina bifida: a few simple facts about a complex condition.