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Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.

In the aftermath of racial justice protests, the country has witnessed a wave of conservative anti-"critical race theory" (CRT) legislation. This essay argues that such legislation is best understood as the latest iteration of a long-standing reactionary political practice. This practice goes back a century to World War I and the 1920s. Then, as now, it was marked by two critical elements: an argument about national identity and a focus on public schools. In the early twentieth century, conservatives began systematically fusing ethno-racial claims about Anglo-European cultural distinctiveness with a self-consciously universal language of the United States as a uniquely free and equal society. They further contended that public schools were failing to adequately teach children in the nation's true values and called for a series of school measures with uncanny resemblances to the present. In exploring this pre-history of today's attacks on public schools, the essay teases out why arguments akin to anti-"CRT" claims initially emerged and recur whenever there have been major flashpoints around cultural and national identity. It also highlights a seemingly paradoxical phenomenon: In the United States, the most prominent defenses of racial hierarchy and attacks on racial reform often speak in a "civic" and ostensibly universal register rather than in an "ethnic" nationalist one. This fact requires Americans to confront the embedded drawbacks of longstanding and taken-for-granted narratives of national purpose, narratives commonly invoked across the political spectrum. [ABSTRACT FROM AUTHOR]

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The article focuses on Left internationalism in the U.S. politics. It mentions it is essential for those on the left to stand in opposition to both imperialism and authoritarianism, while also doing the work of thinking through how to produce conditions of greater global justice, along with the limitations of some traditional positions of the U.S. left.

This keynote speech was delivered on January 31, 2020. It argues that dominant narratives of American legal liberalism and global exceptionalism increasingly find themselves under real political and intellectual strain, even among mainstream scholars and practitioners of constitutional law and public international law. The speech then draws from Critical Race Theory (CRT) and Third World Approaches to International Law (TWAIL) to articulate a competing account of the meaning of American power in the twentieth century, grounded in histories of race and empire. It concludes by reflecting on the current challenges to the established American global legal vision and the potential spaces that may now exist for an alternative politics of transnational solidarity. [ABSTRACT FROM AUTHOR]