We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G2 extending the celebrated T -system relations of type G2. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G2. We use this result to obtain explicit...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

A module M is said to belifting if, for anysubmodule N of M, there exists a direct summand X contained in such that N/X small M/X. satisfy the finite internal exchange propertyif, any and sum decomposition M=Lni=1Mi, M′i Mi (i= 1,2, . , n) M=X⊕(Lni=1M′i). In this paper, we first give characterizations forthe square hollow uniform be lifting (extending). addition, solve negatively question "Does...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

When a virtual machine monitor (VMM) provides code that executes in the context of a guest operating system, allowing that code to have privileged access to specific hardware and VMM resources can enable new mechanisms to enhance functionality, performance, and adaptability. We present a software technique, guarded execution of privileged code in the guest, that allows the VMM to provide this c...

Executing VMM-provided code with privileged access to specific hardware and VMM resources within an untrusted guest operating system can enable new mechanisms to enhance functionality, performance, and adaptability. We present a software technique, guarded execution of privileged code in the guest, that allows the VMM to provide this capability, as well as an implementation for Linux guests in ...

A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...