25,857 research outputs found
On Strongly pi-Regular Rings with Involution
No full textRecall that a ring R is called strongly pi-regular if, for every a in R,there is a positive integer n, depending on a, such that a^n belongs to theintersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study ofthe notion of a strongly pi-star-regular ring, which is the star-version ofstrongly pi-regular rings and which was originally introduced by Cui-Wang in J.Korean Math. Soc. (2015). We also establish various properties of these ringsand give several new characterizations in terms of (strong) pi-regularity andinvolution. Our results also considerably extend recent ones in the subject dueto Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and dueto Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings.Comment: 8 page
On variations of m, n-totally projective Abelian p-groups
No full textWe define some new classes of p-torsion Abelian groups which are closely related to the definitions of n-totally projective, strongly n-totally projective and m, n-totally projective groups introduced by P. Keef and P. Danchev in J. Korean Math. Soc. (2013). We also study their critical properties, one of which is the so-named Nunke's-esque property
Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence.
No full textFor any n ≥ 2 and fixed k ≥ 1, we give necessary and sufficient conditions for an arbitrary nonzero square
matrix in the matrix ring Mn(F) to be written as a sum of an invertible matrix U and a nilpotent matrix N with Nk = 0 over
an arbitrary field F.The first-named author (Peter V. Danchev) was supported in part by the Bulgarian National
Science Fund under Grant KP-06 No. 32/1 of December 07, 2019, as well as by the BIDEB 2221 of TÜBÍTAK,
the second-named author (Esther García) was partially supported by Ayuda Puente 2022, URJC. The three
authors were partially supported by the Junta de Andalucía FQM264
On exchange π-UU unital rings
No full textWe prove that a ring R is exchange 2-UU if, and only if, J(R) is nil and R/J(R)≅B×C, where B is a Boolean ring and C is a ring with C ⊆ Πμ ℤ₃ for some ordinal μ. We thus somewhat improve on a result due to Abdolyousefi-Chen (J. Algebra Appl., 2018) by showing that it is a simple consequence of already well-known results of Danchev-Lam (Publ. Math. Debrecen, 2016) and Danchev (Commun. Korean Math. Soc., 2017).ArticleToyama mathematical journal, vol.39, 2017, Page 1-
Author Peter FitzSimons speaking at the National Library of Australia, Canberra, 13 November 2012 /
No full textTitle from acquisitions documentation.; Part of the collection: Portraits of author Peter FitzSimons speaking at the National Library of Australia, Canberra, 13 November 2012.; Acquired in digital format; access copy available online.; Mode of access: Online.; Photographed by a staff member of the National Library of Australia
О pnBext проективных абелевых p-группах
No full textWe introduce the concept of pnBext projective abelian p-groups and show that they form a class which properly contains the class of all n-balanced projective p-groups. This somewhat enlarges a result due to Keef-Danchev in Houston J. Math. (2012)
COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS
No full textA ring is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring and each abelian group , we find only in terms of , and their sections a necessary and sufficient condition when the group ring is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings
Weakly square-nil-fine rings
No full textWe define a proper subclass of the class of fine rings introduced by Calugareanu-Lam
in J. Algebra Appl. (2017) and completely characterize the new class by showing
that all rings from it are isomorphic to either Z_2 or Z_3. This supplies two recent
publications by Danchev in International Math. Forum (2016, 2017) concerning invo-
fine rings.</jats:p
On weakly clean and weakly exchange rings having the strong property
No full textWe define two classes of rings calling them weakly clean rings and weakly
exchange rings both equipped with the strong property. Although the classes
of weakly clean rings and weakly exchange rings are different, their two
proper subclasses above do coincide. This extends results due to W. Chen
(Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also
completely characterize strongly invo-regular rings, thus somewhat extending
results due to Danchev-McGovern (J. Algebra, 2015). Some other principal
results concerning weakly clean and weakly exchange rings are discussed as
well.</jats:p
О pnBext проективных абелевых p-группах
No full textWe introduce the concept of pnBext projective abelian p-groups and show that they form a class which properly contains the class of all n-balanced projective p-groups. This somewhat enlarges a result due to Keef-Danchev in Houston J. Math. (2012)
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