We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz–Happel’s theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen–Macaulay modules. Three concrete examples of finitedim...

Associating to each pre-order on the indices 1; :::;n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n n matrix rings. Rings within the order-convex hull of the embedding, i.e. matrix rings that contain the ring of diagonal matrices, can be viewed as incidence algebras of ideal-valued, generalized pre-order relation...

In this paper, we present a study of tuneable equilateral triangular shaped spilt ring resonator (ETSRR). In this ETSRR we rotate the inner and outer rings by varying the position of the splits in rings. For this we used radio frequency microelectromechanical system (RF MEMS) switches. By making MEMS switches ON/OFF, the positions of splits in the rings were varied which can be considered as ro...

In this note, we introduce the concept of semi-*-IFP, involutive version semi-IFP, which is a generalization quasi-*-IFP and *-reducedness *-rings. We study basic structure properties *-rings having semi-*-IFP give results for IFPs in rings with involution. Several counterexamples are stated to connect versions IFP. discuss conditions be extended into *-subrings ring upper triangular matrices. ...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

Trinion and Quaternion numbers are one of the hypercomplex which is an extensions complex number. From numbers, a bimodule can be formed ordered pair Quaternion. Furthermore, number, their into Formal Triangle Matrix. The Matrix better known as Upper Since number rings, then called Triangular Ring. purpose this study to construct Armendariz Ring using obtained results will show that Rings -Skew...

We consider wreath product decompositions for semigroups of triangular matrices. We exhibit an explicit wreath product decomposition for the semigroup of all n× n upper triangular matrices over a given field k, in terms of aperiodic semigroups and affine groups over k. In the case that k is finite this decomposition is optimal, in the sense that the number of group terms is equal to the group c...