The Cohen-Macaulay representation type of arithmetically Cohen-Macaulay varieties

We show that all reduced closed subschemes of projective space that have a Cohen-Macaulay graded coordinate ring are of wild Cohen-Macaulay type, except for a few cases which we completely classify.

ANALISIS KEMAMPUAN MULTI REPRESENTASI PESERTA DIDIK PADA MATERI USAHA DI MADRASAH ALIYAH

The purpose of this study to identify student's multi-representation ability about work at MA Negeri Bengkayang. The method used is the survey method without comparative group which is descriptive correlative with research instrument in the form of descriptive test on the multi-representation ability test of five questions and multiple-choice test on the learning outcomes test often questions. the validity of the multi-representation test was 3.45 whit valid criteria and the validity of the learning outcomes test was 3.52 with valid criteria Meanwhile, the reliability of the multi-representation test was 0.516 in the sufficient category and the reliability of the learning outcomes test was 0.55 in the sufficient category. The study found that the multi-representation ability of students was low with an average percentage of 33.08%. The multi-representation ability of students with the highest percentage is in the image to symbol representation type, which is 75%, while the multi-representation ability of students with the lowest percentage is in the verbal to mathematical representation type, which is 5.19%. This study also did not found a correlation (r count 0.04 > r table 0.4848) between multi-representation ability and student's learning outcomes. The result of this study is expected to be taken into consideration in determining learning strategies.Keywords: Work, Multi-representation Ability, Learning Outcomes

τ-Rigid Modules for Algebras with Radical Square Zero

For a radical square zero algebra [Formula: see text] and an indecomposable right [Formula: see text]-module [Formula: see text], when [Formula: see text] is Gorenstein of finite representation type or [Formula: see text] is [Formula: see text]-rigid, [Formula: see text] is [Formula: see text]-rigid if and only if the first two projective terms of a minimal projective resolution of [Formula: see text] have no non-zero direct summands in common. In particular, we determine all [Formula: see text]-tilting modules for Nakayama algebras with radical square zero.

Igusa-Todorov function on path rings

The aim of this paper is to study the relation between the Igusa-Todorov functions for $A$, a finite dimensional algebra, and the algebra $AQ$. In particular it is proved that $\fidim (AQ) = \fidim (A) + 1$ when $A$ is a Gorenstein algebra. As a consequence of the previous result, it is exhibited an example of a family of algebras $\{A_n\}_{n \in \mathbb{N}}$ such that $\fidim (A_n) = n$ and each $A_n$ is of $\Omega^{\infty}$-infinite representation type.