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In this article we study various conditions on a unital prime Banach algebra that ensure its commutativity. More specifically, we prove that a unital prime Banach algebra Awith a nonzero continuous linear generalized derivation gassociated with a nonzero linear continuous derivation dsatisfying either $$g((xy)^n)-d(x^n)d(y^n)\in Z(A)$$ g((xy)n)-d(xn)d(yn)∈Z(A) or $$g((xy)^n)-d(y^n)d(x^n)\in Z(A)$$ g((xy)n)-d(yn)d(xn)∈Z(A) , for sufficiently many x, yand an integer $$n=n(x,y)>1$$ n=n(x,y)>1 is commutative.

The latissimus dorsi is the larger, flat, dorso-lateral muscle on the trunk, posterior to the arm, and partly covered by the trapezius on its median dorsal region. Origin of the latissimus dorsi is from spinous processes of thoracic T7–T12, thoracolumbar fascia, iliac crest and inferior 3 or 4 ribs, inferior angle of scapula and insertion on floor of intertubercular groove of the humerus. We have studied 50 cadavers in the different medical colleges in which we found 2% case of anterior and posterior slip of the muscle fibers with their extension up to the pectoralis major and teres major respectively. Usually, latissimus dorsi involve in extension, adduction, transverse extension also known as horizontal abduction, flexion from an extended position, and internal rotation of the shoulder joint. It also has a synergistic role in extension and lateral flexion of the lumbar spine. The latissimus dorsi may be used for the tendon graft surgeries. Tight latissimus dorsi has been shown to be one cause of chronic shoulder pain and chronic back pain. Because the latissimus dorsi connects the spine to the humerus, tightness in this muscle can manifest as either sub-optimal glenohumeral joint function (which leads to chronic shoulder pain) or tendinitis in the tendinous fasciae connecting the latissimus dorsi to the thoracic and lumbar spine. Latissimus dorsi used for pedicle transplant rotator cuff repair reconstruction of breast, face, scalp and cranium defect. The extra slip of the latissimus dorsi may puzzle any transplant operations. We as anatomist discuss the clinical implication of the extra slip of latissimus dorsi.