In this paper, we investigate the notions of X ⊥ -projective, id="M2"> -injective, and id="M3"> -flat modules give some characterizations these modules, where id="M4"> is a class left modules. We prove that all id="M5"> -projective Kaplansky. Further, if id="M6"...

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of RR into R (N) R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is...

Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...

The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove t...

We define a faithful linear monoidal functor from the partition category, and hence Deligne’s category $\mathrm{\underline{Re}p}(S\_t)$, to additive Karoubi envelope of Heisenberg category. show that induced map on Grothendieck rings is injective corresponds Kronecker coproduct symmetric functions.

For a long period the theory of modules over rings on the one hand and comodules and Hopf modules for coalgebras and bialgebras on the other side developed quite independently. In this talk we want to outline how ideas from module theory can be applied to enrich the theory of comodules and vice versa. For this we consider A-corings C with grouplike elements over a ring A, in particular Galois c...

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

The symmetric group S(n) is partially ordered by Bruhat order. This order is extended by L. Renner to the set of partial injective functions of {1, 2, . . . , n} (see, Linear Algebraic Monoids, Springer, 2005). This poset is investigated by M. Fortin in his paper The MacNeille Completion of the Poset of Partial Injective Functions [Electron. J. Combin., 15, R62, 2008]. In this paper we show tha...