1,720,982 research outputs found
Cofinitely weak supplemented lattices
No full textIn this paper it is shown that an E-complemented complete modular lattice L with small radical is weakly supplemented if and only if it is semilocal. L is a cofinitely weak supplemented lattice if and only if every maximal element of L has a weak supplement in L. If )α/0 is a cofinitely weak supplemented (weakly supplemented) sublattice and 1/α has no maximal element (1/α is weakly supplemented and a has a weak supplement in L), then L is cofinitely weak supplemented (weakly supplemented)
Absolute co-supplement and absolute co-coclosed modules
No full textA module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.Scientific and Technical Research Council of Turke
Absolute co-supplement and absolute co-coclosed modules
Get PDFA module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.Scientific and Technical Research Council of Turke
Cofinitely Supplemented Modular Lattices
Get PDFIn this paper it is shown that a lattice L is a cofinitely supplemented lattice if and only if every maximal element of L has a supplement in L. If a/0 is a cofinitely supplemented sublattice and 1/a has no maximal element, then L is cofinitely supplemented. A lattice L is amply cofinitely supplemented if and only if every maximal element of L has ample supplements in L if and only if for every cofinite element a and an element b of L with a v b there exists an element c of b/0 such that a v c where c is the join of finite number of local elements of b/0. In particular, a compact lattice L is amply supplemented if and only if every maximal element of L has ample supplements in L
Noetherian and Artinian Lattices
Get PDFIt is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements
Cofinitely weak f-supplemented lattices
No full textIn this paper, weakly f-supplemented and cofinitely weak f-supplemented lattices are introduced and studied. Let a be an element of L such that a <fL. If 1/a is weakly (f ∧ a)-supplemented and a/0 is weakly (f ∨ a)-supplemented, then L is weakly f-supplemented. A d-complemented lattice with f-small f-radical is weakly f-supplemented if and only if L is f-semilocal. A lattice L is cofinitely weak f-supplemented if and only if every maximal element of L has a weak f-supplement in L. If a/0 is a cofinitely weak (f ∨ a)-supplemented sublattice of a lattice L and 1/a has no maximal element, then L is cofinitely weak f-supplemented. Let L be a compactly generated lattice such that for every compact element c of L, rad(f∨c)(c/0) = c ∨radf(L). Then L is cofinitely weak f-supplemented if and only if L is cofinitely (f ∨ c)-supplemented. Let L be a compact lattice such that for every compact element c of L, rad(f∨c)(c/0) = c ∨radf(L). Then L is weakly f-supplemented if and only if L is (f ∨ c)-supplemented
Kafeslerde tümleyenler
No full textBu tezde temel olarak tümlenmiş, zayıf tümlenmiş, bol tümlenmiş, eşsonlu tümlenmiş, eşsonlu zayıf tümlenmiş ve bol eşsonlu tümlenmiş modüller hakkında bilinen sonuçların kafes teorisine genelleştirilmesi üzerine çalışılması amaçlanmıştır. L, en büyük elemanı 1 en küçük elemanı 0 olan tam modüler bir kafes olsun. Bir modülün herhangi bir küçük alt modülünün bir modül homomorfizması altındaki görüntüsü de küçük alt modüldür. Bu özellik kafeslerde her zaman doğru değildir. Bir modülün alt modülleri kafesi pseudo-bütünlenmiştir. Bu özellik her kafes için sağlanmak zorunda değildir. 1/a ve a/0 bölüm alt kafesleri zayıf tümlenmiştir ve a’nın L’de bir zayıf tümleyeni varsa L kafesi de zayıf tümlenmiştir. L kafesinin bol tümlenmiş olması için gerek ve yeter koşul zayıf tümlenmiş olması ve L’nin her elemanının L’de bir eşkapanışının var olmasıdır. L kafesinin eşsonlu tümlenmiş (zayıf tümlenmiş) olması için gerek ve yeter koşul her maksimal elemanının L’de bir tümleyeninin (zayıf tümleyeninin) olmasıdır. Sonlu sayıda eşsonlu tümlenmiş (zayıf tümlenmiş) kafeslerin supremumu da eşsonlu tümlenmiştir (zayıf tümlenmiştir). a/0, L’nin eşsonlu tümlenmiş (zayıf tümlenmiş) bir alt kafesi ve 1/a’da hiç maksimal eleman yok ise L kafesi de eşsonlu tümlenmiştir (zayıf tümlenmiştir). Kompakt üretilmiş kafeslerde eşsonlu elemanların zayıf tümleyenleri kompakt elemanlar olarak kabul edilebilir. Bu özellik kompakt üretilmiş olmayan kafesler için doğru değildir. L kafesinin bol eş-sonlu tümlenmiş olması için gerek ve yeter koşul her maksimal elemanının L’de bol tümleyenlerinin olmasıdır. Kompakt bir L kafesinin bol tümlenmiş olması için gerek ve yeter koşul her maksimal elemanının L’de bol tümleyenlerinin olmasıdır
Purely Rickart and Dual Purely Rickart Objects in Grothendieck Categories
No full textIn this paper, (dual) purely Rickart objects are introduced as generalizations of (dual) Rickart objects in Grothendieck categories. Examples showing the relations between (dual) relative Rickart objects and (dual) relative purely Rickart objects are given. It is shown that in a spectral category (dual) relative purely Rickart objects coincide with (dual) relative Rickart objects. (Co)products of (dual) relative purely Rickart objects are studied. Classes all of whose objects are (dual) relative purely Rickart are identified. It is shown how this theory may be employed in order to study (dual) relative purely Baer objects in Grothendieck categories. Also applications to module and comodule categories are given.</div
- …
