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<div>Dear colleagues,</div>
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<p>You are cordially invited to the general <span class="m_5448320135740532138m_6472383400221921050il">seminar</span> organized by the Department of Mathematics, Atılım University.<br /><br />Our speaker is<strong> Yosum Kurtulmaz , </strong>Bilkent University<strong>.</strong></p>
<p>The title of her talk is <strong>"<span>VERY CLEANNESS OF GENERALIZED MATRICES</span>"</strong>. </p>
<p>You can find the abstract of her talk below.</p>
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<p>Abstract: <span>An element $a$ in a ring $R$ is very clean in case there exists</span><br /><span>an idempotent $e\in R$ such that $ae = ea$ and either $a- e$ or $a</span><br /><span>+ e$ is invertible. An element $a$ in a ring $R$ is very $J$-clean</span><br /><span>provided that there exists an idempotent $e\in R$ such that $ae =</span><br /><span>ea$ and either $a-e\in J(R)$ or $a + e\in J(R)$. Let $R$ be a</span><br /><span>local ring, and let $s\in C(R)$. We prove that $A\in K_s(R)$ is</span><br /><span>very clean if and only if $A\in U(K_s(R))$; $I\pm A\in U(K_s(R))$</span><br /><span>or $A\in K_s(R)$ is very J-clean.</span></p>
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<div><strong>Date: December 06, 2017</strong></div>
<p><strong>Time: <span class="m_5448320135740532138aBn"><span class="m_5448320135740532138aQJ"><span class="aBn"><span class="aQJ">15:40</span></span></span></span></strong></p>
<p><strong>Place: FEF 404</strong></p>
<div>With my best regards,</div>
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<div>Burcu Gülmez Temür</div>
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