1,721,529 research outputs found
-Differential Identities of
No full textLet δ and ε be the inner derivations of UT m(F) induced by the unit matrices e 1m and e mm respectively. We study the differential polynomial identities of the algebra UT m(F) under the coupled action of δ and ε. We produce a basis of the differential identities, then we determine the S n-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence
Differential polynomial identities of upper triangular matrices of size three
No full textWe determine the differential polynomial identities of upper triangular matrices over a base field of characteristic zero, under the action of its full Lie algebra of derivations. We compute the exact differential codimension sequence of the multilinear ones and describe their -structure by means of an explicit decomposition of the -cocharacter of their proper part
Role of echocardiography for the assessment of left ventricular dysfunction due to cancer treatments
No full textThe use of echocardiography for the assessment of patients undergoing potentially cardiotoxic cancer treatments and for follow-up of treated patients is increasing and has become a significant public health problem due to the need for repeated examinations over time. Despite the technological advances of echocardiography, there are still uncertainties about how best to use this technique to identify and guide the management of cardiotoxicity. The purpose of this article is to discuss the role of echocardiography in the study of ventricular dysfunction due to cancer treatments, with the aim to clarify the main echocardiographic information to be provided, the methods to apply and the strategies to implement to streamline as much as possible the use of echocardiography in the field of cardioncology
Le estrazioni petrolifere in Basilicata tra opposizione e interventi di compensazione
No full textVal d’Agri is an area of the province of Potenza interested for about twenty years by the extraction of oil and gas. The volumes of hydrocarbons that are ex-tracted amount today to 7% of oil and gas consumption in Italy. In 1998, some years after the beginning of this activity and in anticipation of its growth, Eni and Basilicata Region signed an agreement which contains several measures of com-pensation over royalties. This type of activity (along with the first oil treatment in the Oil Center) pro-duced initially forms of opposition from environmental groups, which led to com-mittees and associations, born in the last years. Yet the response of the local popu-lation to these initiatives has been weak. We argue that different measures of com-pensation, although considered insufficient so far, have contributed to contain the protests. However, plans for a further expansion of extraction and some events af-fecting the state of the environment and the protection of health are increasing awareness of the risks and impacts associated with this activity
ON THE EXISTENCE OF THE GRADED EXPONENT FOR FINITE DIMENSIONAL -GRADED ALGEBRAS
No full textLet F be an algebraically closed field of characteristic zero, and let A be an associative unitary
F-algebra graded by a group of prime order. We prove that if A is finite dimensional then the graded
exponent of A exists and is an integer
On the *-polynomial identities of a class of *-minimal algebras
No full textThe problem of classifying the finite dimensional *-minimal algebras up to *-PI equivalence has been recently faced by Di Vincenzo and Spinelli. Essentially, if A is a finite dimensional *-minimal algebra over the field F then there exists an n-tuple (A_1,..., A_n) of *-simple algebras allowing the construction of a block-matrix algebra UT_*(A_1,...,A_n) which is *-PI equivalent to A, that is the algebras satisfy the same *-polynomial identities. The simplest case is when A_i = F, for all i. In this case we denote by U_n the algebra UT_*(F,..., F) a sub-algebra of the full matrix algebra M_2n(F).
In the present article, we study the *-polynomial identities of U_n. We prove that T_*(U_n) is generated by a single explicit polynomial as soon as F is an infinite field of characteristic different from 2. Moreover, in the case char. F = 0, we describe the structure of T_*(U_n) under the action of general linear group
-graded cocharacters for superalgebras of triangular matrices
No full textLet K be a field of characteristic zero, let A, B be K-algebras with polynomial identities and let M be a free (A; B)-bimodule. The algebra R of 2x2 upper triangular matrices, having the elements of the algebras A and B on the main diagonal and the elements of the free module M on the (1,2) position
can be endowed with a natural Z2-grading.
In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices over the field K. In particular, we completely classify these invariants for the algebra of 3 × 3 upper triangular matrices endowed with all possible Z2-gradings
Differential Polynomial Identities of Upper Triangular Matrices Under the Action of the Two-Dimensional Metabelian Lie Algebra
No full textWe study the differential polynomial identities of the algebra UTm(F) under the derivation action of the two dimensional metabelian Lie algebra, obtaining a generating set of the TL-ideal they constitute. Then we determine the Sn-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence
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