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Linear and Multilinear Algebra, ISSN 0308-1087, 2019, pp. 1 - 9
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 06/2020, Volume 224, Issue 6, p. 106271
Let T=(A0UB) be a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. Let C1 and C2 be two classes of left A-modules, D1 and D2... 
Precover | Formal triangular matrix ring | Cotorsion pair | Preenvelope | MATHEMATICS | MATHEMATICS, APPLIED | MODULES
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 04/2020, Volume 224, Issue 4, p. 106207
Let T=(A0UB) be a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. We prove that, if T is a right coherent ring, UB has finite... 
Gorenstein flat module | Gorenstein flat dimension | Formal triangular matrix ring | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 01/2013, Volume 438, Issue 1, pp. 250 - 260
Let R and S be rings with identity, M be a unitary (R,S)-bimodule, and T=RM0S be the upper triangular matrix ring determined by R,S and M. Let Eij be the... 
Prime ring | Derivation | Biderivation | Triangular matrix ring | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | GENERALIZED BIDERIVATIONS | COMMUTING MAPS | CENTRALIZING MAPPINGS | PRIME-RINGS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2016, Volume 493, pp. 580 - 605
Let R be a subring of a ring Q, both having the same unity. We prove that if R is a d-free subset of Q, then the upper triangular matrix ring Tn(R) is a d-free... 
Functional identity | d-Free subset | Upper triangular matrix ring | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Aequationes Mathematicae, ISSN 0001-9054, 06/2017, Volume 91, Issue 3, pp. 563 - 578
Let T-n (R) be the upper triangular matrix ring over a unital ring R. Suppose that B : Tn (R) x Tn (R) is a biadditive map such that B(X, X) X = X B(X, X) for... 
trace of a biadditive map | Upper triangular matrix ring | functional identity | commuting map | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | MAPS | CENTRALIZING TRACES | LIE TRIPLE ISOMORPHISMS | MAPPINGS | FUNCTIONAL IDENTITIES
Journal Article
Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 12/2019, Volume 50, Issue 4, pp. 837 - 847
We obtained several equivalent conditions for the existence of core inverses and dual core inverses of triangular matrices over a ring with involution. As... 
dual core inverse | ring | Numerical Analysis | Mathematics, general | Mathematics | group inverse | Applications of Mathematics | Core inverse | triangular matrix | MATHEMATICS | INVERSE
Journal Article
Algebra Colloquium, ISSN 1005-3867, 06/2015, Volume 22, Issue 2, pp. 271 - 280
Let R be a ring with an endomorphism sigma. We show that the clean property and various Armendariz-type properties of R are inherited by the skew matrix rings... 
clean ring | triangular matrix ring | quasi-Armendariz ring | MATHEMATICS | QUASI-BAER RINGS | CLEAN RINGS | MATHEMATICS, APPLIED | EXCHANGE RINGS | ARMENDARIZ RINGS | EXTENSIONS
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 05/2017, Volume 65, Issue 5, pp. 882 - 890
Every matrix in the triangular matrix ring over a bleached local ring R is similar to a 'simple form', which is, in most cases, contained in a subring of with... 
bleached local ring | strongly clean ring | Triangular matrix ring | 16U60 | strong 2-sum property | 16U99 | Primary: 16L30 | MATHEMATICS | ELEMENTS | UNIT | STRONGLY CLEAN RINGS | IDEMPOTENT | SUM | Theorems | Algebra | Bleaching | Theorem proving | Images | Cases (containers) | Handling | Rings (mathematics)
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2016, Volume 507, pp. 132 - 136
Let Nr, r≥4, be the ring of strictly upper triangular matrices with entries in a field F of characteristic zero. We describe all linear maps f:Nr→Nr satisfying... 
Commuting maps | Upper triangular matrices | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 3/2019, Volume 25, Issue 1, pp. 87 - 96
Let R be a ring and $$\delta $$ δ is a derivation of R. In this paper, it is proved that, under suitable conditions, the differential polynomial ring... 
Semicentral idempotent | Piecewise prime ring | Primary 16W60 | Secondary 16P40 | Quasi-Baer ring | Differential polynomial ring | Triangulating dimension | 16W70 | Generalized triangular matrix representation | Mathematics, general | Mathematics | 16S36
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 06/2015, Volume 52, Issue 4, pp. 781 - 795
Given a positive integer n, a ring R is said to be n-semi-Armendariz if whenever f(n) = 0 for a polynomial f in one indeterminate over R, then the product... 
N-semi-Armendariz ring | Upper triangular matrix ring | Semi-Armendariz ring | MATHEMATICS | semi-Armendariz ring | MATHEMATICS, APPLIED | upper triangular matrix ring | n-semi-Armendariz ring | GAUSSIAN RINGS
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 02/2019, Volume 67, Issue 2, pp. 348 - 359
The aim of this paper is to give an improvement of a result on functional identities in upper triangular matrix rings obtained by Eremita, which presents a... 
Functional identity | d-free subset | upper triangular matrix ring | 16R60 | 16R50 | MATHEMATICS | Rings (mathematics)
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 02/2020, Volume 587, pp. 387 - 391
There is an error in the proof of Theorem 2.3 of [1]. In this corrigendum Theorem 2.3 is rewritten and Theorem 2.5 and Theorem 1.1 of [1] are reproved. 
Triangular matrices | Infinite matrices | Products of involutions | Products of coninvolutions | Mathematical analysis | Matrix methods | Linear algebra | Rings (mathematics)
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2012, Volume 436, Issue 9, pp. 3692 - 3700
A ring is called a left p.p. ring if every principal left ideal is projective. The objective here is to completely determine the left p.p. structural matrix... 
von Neumann regular ring | p.p. ring | Structural matrix ring | Triangular matrix ring | MATHEMATICS, APPLIED | RADICALS
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 03/2017, Volume 65, Issue 3, pp. 572 - 581
Let be a finite field with q elements, be the ring of all matrices over , Z(R) be the set of all zero-divisors of R, i.e. Z(R) consists of all singular... 
05C50 | Total graph over a ring | automorphisms of graphs | 15A15 | clique number | 05C35 | 20H20 | MATHEMATICS | COMMUTATIVE RING | ALGEBRAS | UPPER-TRIANGULAR MATRICES | REGULAR GRAPHS | ZERO-DIVISOR GRAPH | CHROMATIC NUMBER | Algebra | Mathematical analysis | Images | Graphs | Graph theory | Automorphisms | Rings (mathematics)
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 12/2013, Volume 439, Issue 12, pp. 4063 - 4069
In this paper we investigate Jordan homomorphisms of upper triangular matrix rings and give a sufficient condition under which they are necessarily... 
Upper triangular matrix ring | Homomorphism | Triangular ring | Jordan homomorphism | Anti-homomorphism | MATHEMATICS, APPLIED | ALGEBRAS | SEMIPRIME RINGS | ISOMORPHISMS | MAPPINGS
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2012, Volume 40, Issue 2, pp. 784 - 794
A ring R is quasipolar if for any a ∈ R, there exists p 2  = p ∈ R such that , a + p ∈ U(R) and ap ∈ R qnil . In this article, we investigate conditions on a... 
16S99 | Quasipolar ring | Triangular matrix ring | Strongly clean ring | Local ring | 16U99 | 15A09 | MATHEMATICS | STRONGLY CLEAN MATRIX
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2013, Volume 438, Issue 11, pp. 4374 - 4381
We describe isomorphisms between strongly triangular matrix rings that were defined earlier in Birkenmeier et al. (2000) [3] as ones having a complete set of... 
Semicentral idempotent | Semicentral reduced ring | Bimodule isomorphism | Triangular matrix ring | MATHEMATICS, APPLIED | REPRESENTATIONS
Journal Article
Russian Mathematics, ISSN 1066-369X, 12/2017, Volume 61, Issue 12, pp. 73 - 79
Abstract—In a paper published in 2008 P. A. Krylov showed that formal matrix rings Ks(R) and Kt(R) are isomorphic if and only if the elements s and t differ up... 
formalmatrix ring | generalized incidence algebra | Mathematics, general | Mathematics | upper triangular matrix ring | isomorphism problem | zero trace ideals | incidence algebra | Algebra
Journal Article
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