On the relation between K-flatness and K-projectivity
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DOI: 10.1016/j.jalgebra.2018.10.004
Abstract: Abstract Krause [19] has proved that the homotopy category K ( R - PureProj ) of pure projective modules over an associative ring R is compactly generated and equivalent to the Verdier quotient K (… read more here.
Keywords: projective modules; relation flatness; flatness projectivity; homotopy category ... See more keywords
Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings
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DOI: 10.1016/j.jalgebra.2022.03.009
Abstract: We apply set-theoretic methods to study projective modules and their generalizations over transfinite extensions of simple artinian rings R. We prove that if R is small, then the Weak Diamond implies that projectivity of an… read more here.
Keywords: projective modules; artinian rings; simple artinian; projectivity ... See more keywords
On the structure of pure-projective modules and some applications
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DOI: 10.1016/j.jpaa.2016.08.012
Abstract: Abstract We study direct-sum decompositions of pure-projective modules over some classes of rings. In particular, we determine several classes of rings over which every pure-projective left module is a direct sum of cyclic modules. Finally,… read more here.
Keywords: structure pure; modules applications; pure; projective modules ... See more keywords
Generalizations of projectivity and supplements revisited for superfluous ideals
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DOI: 10.1080/00927872.2018.1468897
Abstract: Abstract We (re)introduce four ideal-related generalizations of classic module-theoretic notions: the ideal-superfluity, projective ideal-covers, the ideal-projectivity, and ideal-supplements. For a superfluous ideal I, the main theorem asserts the equivalence between the conditions: “I-supplements are direct… read more here.
Keywords: projectivity supplements; generalizations projectivity; ideal; finitely generated ... See more keywords
A description of Gorenstein projective modules over the tensor products of algebras
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DOI: 10.1080/00927872.2018.1539172
Abstract: Abstract Let A be a two-sided coherent algebra over a field k and B be a finite-dimensional algebra. If B is Gorenstein, we give a description of finitely presented Gorenstein projective modules over the tensor… read more here.
Keywords: modules tensor; projective modules; gorenstein projective; description ... See more keywords
Gorenstein projective modules and recollements over triangular matrix rings
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DOI: 10.1080/00927872.2020.1775240
Abstract: Abstract Let be a triangular matrix ring with R and S rings and an R–S-bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions… read more here.
Keywords: triangular matrix; recollements triangular; projective modules; gorenstein projective ... See more keywords
Differential projective modules over differential rings, II
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DOI: 10.1080/00927872.2022.2045493
Abstract: Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the quotient monoid… read more here.
Keywords: monoid; differential rings; projective modules; differential projective ... See more keywords
Subprojectivity domains of pure-projective modules
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DOI: 10.1142/s0219498820500917
Abstract: In a recent paper, Holston et al. have defined a module [Formula: see text] to be [Formula: see text]-subprojective if for every epimorphism [Formula: see text] and homomorphism [Formula: see text], there exists a homomorphism… read more here.
Keywords: subprojectivity; projective modules; pure projective; formula see ... See more keywords
On MF-projective modules
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DOI: 10.15672/hujms.731098
Abstract: In this paper, we study left orthogonal class of max-flat modules which are the homological objects related to s-pure exact sequences of modules and module homomorphisms. Namely, a right module A is called MF-projective if… read more here.
Keywords: max flat; projective modules; modules projective;
Some infinitely generated non-projective modules over path algebras and their extensions under Martin's axiom
Sign Up to like & getrecommendations! Published in 2020 at "Journal of The Mathematical Society of Japan"
DOI: 10.2969/jmsj/79857985
Abstract: In this paper it is proved that, when $Q$ is a quiver that admits some closure, for any algebraically closed field $K$ and any finite dimensional $K$-linear representation $\mathcal{X}$ of $Q$, if ${\rm Ext}^1_{KQ}(\mathcal{X},KQ)=0$ then… read more here.
Keywords: martin axiom; projective modules; non projective; infinitely generated ... See more keywords