Yazar "Kosan, M. Tamer" seçeneğine göre listele

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    Kernel-endoregular modules and the morphic property
    (Taylor & Francis Inc, 2024) Tasdemir, Ozgur; Kosan, M. Tamer
    This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands (less than or similar to circle plus):(1) The condition that whenever (Im lambda congruent to)M/Ker lambda less than or similar to M-circle plus then Ker lambda and Im lambda are direct summands of M for any endomorphism lambda is an element of End(M) (kernel-endoregular modules).(2)The condition that if M/A congruent to B where A, B less than or similar to M-circle plus then M/B congruent to A (iso-summand-morphic modules).(3 )The condition if M/A congruent to B where A, B <= M-circle plus , then M/B congruent to A (summand-morphic modules) which is precisely the internal cancellation property for modules.
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    On modules and rings having large absolute direct summands
    (Taylor & Francis Inc, 2023) Dao Thi, Trang; Kosan, M. Tamer; Tasdemir, Ozgur; Quynh, Truong Cong
    An ADS module is a direct sum of mutually injective modules, and an e-ADS module is a direct sum of mutually automorphism-invariant modules. In this paper, we introduce and study large ADS (LADS) modules that form a class of modules larger than ADS modules. An LADS module is a direct sum of mutually essentially injective modules. This result corresponds to the results of ADS and e-ADS modules.Communicated by Toma Albu
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    On modules and rings in which complements are isomorphic to direct summands
    (Taylor & Francis Inc, 2022) Karabacak, Fatih; Kosan, M. Tamer; Quynh, T. Cong; Tasdemir, Ozgur
    A right R-module M is virtually extending (or CIS) if every complement submodule of M is isomorphic to a direct summand of M, and M is called a virtually C2-module if every complement submodule of M which is isomorphic to a direct summand of M is itself a direct summand. The class of virtually extending modules (respectively, virtually C2-modules) is a strict and simultaneous generalization of extending modules (respectively, unifies extending modules and C2-modules): M is a semisimple module if and only if M is virtually semisimple and C2, and M is an extending module if and only if M is virtually extending and virtually C2. Furthermore, every virtually simple right R-module is injective if and only if R is a right V-ring and the class of virtually simple right R-modules coincides with the class of simple right R-modules. Among other results, we show that (1) if all cyclic sub-factors of a cyclic weakly co-Hopfian right R-module M are virtually extending, then M is a finite direct sum of uniform submodules; (2) every distributive virtually extending module over any Noetherian ring is a direct sum of uniform submodules; (3) over a right Noetherian ring, every virtually extending module satisfies the Schroder-Bernstein property; (4) being virtually extending (VC2) is a Morita invariant property; (4) if M circle plus E(M) is a VC2-module where E(-) denotes the injective hull, then M is injective.